ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Solving Geometry Problems Involving System of Equations In Two Variables

Updated on August 6, 2011

Solving Geometry Problems Involving System of Equations In Two Variables

Algebra has also found wide applications in Geometry. Among its common problems are problems involving perimeters and angles. In this hub I included five sample problems involving perimeter and angles.

Sample Problem Number One :

A rectangular garden has a perimeter of 100 meters. The length is four times its width. Find the dimensions of the garden.

Solution :

Let X = width

Let Y = length

P = 2L + 2w

Equation one : 2X + 2Y = 100

Equation Two : Y = 4X

Substitute equation two in equation one :

2X + 2 (4X) = 100

2X + 8X = 100

10X = 100

(1/10) 10X = 100 (1/10)

X = 10 ==è width

4X = 4 (10) = 40 ==è lenth

Sample Problem Two :

The perimeter of a rectangular picture frame is 80 centimeter. Two times the width is equal to the length increased by five. Find its dimensions.

Solution :

Let X = width

Let Y = length

P = 2L + 2W

Equation one : 2X + 2Y = 80

Equation two: 2X = Y + 5

We use elimination method by subtraction to solve for the unknown variables.

2X + 2Y = 80

(-)2X (+) -Y = (-) 5

3Y = 75

(1/3) 3Y = 75 (1/3)

Y = 25 ==è length

To solve for width substitute in equation two

2X = 25 + 5

2X = 30

X = 15 ====è width

Sample Problem Three:

The perimeter of a rectangular flower garden is 120 meters. The length is ten meters greater than its width. Find its dimensions.

Solution :

Let X = width

Let Y = length

P = 2L +2W

Equation one : 2X + 2Y = 120

Equation two : Y = X + 10

Substitute equation two in equation one :

2X + 2 (X + 10 ) = 120

2X + 2X + 20 = 120

4X = 120 – 20

4X = 100

(1/4) 4X = 100 (1/4)

X = 25 ==è width

Y = 25 + 10 = 35 ===è lenth

Sample Problem Number Four :

The sum of the two nonright angles in a right triangle is of course 90 degrees. If twice the first is 40 degrees more than three times the second. Find the measurement of the angles of the right triangle.

Solution :

Let X = first angle

Let Y = second angle

Equation one : X + Y = 90

Equation two : 2X = 3Y + 40

From equation one we derive Y = 90 – X the substitute this in equation two.

2X = 3(90-X) + 40

2X = 270 – 3X + 40

2X + 3X = 270 + 40

5X = 310

(1/5) 5X = 310 (1/5)

X = 62 degrees ===è first angle

Y = 90 – 62 = 28 ===è second angle

Sample Problem Number Five :

Two angles are supplementary. The bigger angle is thrice as large as the smaller angle. Find the measurement of the angles.

Solution :

Let X = smaller angle

Let Y = bigger angle

The two angles are supplementary it means that their sum is equal to 180 degrees.

Equation one : X + Y = 180

Equation two : Y = 3X

Substitute equation two in equation one :

X +3X = 180

4X = 180

(1/4) 4X = 180 (1/4)

X = 45 ==èsmaller angle

Y = 3(45) = 135 ====. Bigger angle


    0 of 8192 characters used
    Post Comment

    • profile image


      5 years ago

      it is very great i really like iit

    • profile image

      John Peterson 

      6 years ago


    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      7 years ago from Manila

      Hi DeBorrah I am glad to hear from you again. Thank you for appreciating this hub. Your visit and comments are much appreciated. You have been really a great encouragement to me. Blessings to you and your family. Best regards.

    • DeBorrah K. Ogans profile image

      DeBorrah K Ogans 

      7 years ago

      Cristina, Nice Geometry lesson... You are so smart intellectually and gifted spiritually! What a double blessing that you also Love the Lord!

      Thank You for sharing, In HIS Love, Grace, Joy, Peace & Blessings!


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

    Show Details
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)