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Solving Word Problems Involving Quadratic Equations

Updated on August 6, 2018

Solving Word Problems Involving Quadratic Equation

One of the most important topics in Algebra is solving quadratic equations. It has found wide applications in many areas of Mathematics. This hub presents several problems involving quadratic equations with their solution. Hope you will enjoy this.

Sample Problem One :

The sum of two numbers is 18 and the sum of their square is 170. Find the numbers.


Let X = the first number

18 – X = the second number

X^2 = square of the first number

(18-X)^2 = square of the second number

Working Equation:

X^2 + (18-X)^2 = 170

X^2 + 324 -36X + X^2 = 170

2X^2 -36X +324 -170 = 0

(2X^2 -36X + 154 = 0)1/2

X^2 – 18X + 77 = 0

Factoring X^2 -18X + 77 = 0

(X – 7) (X – 11) = 0

X – 7 = 0 therefore X = 7

X – 11 = 0 therefore X = 7

The two number are 7 and 11.

Problem Number Two :

One leg of a right triangle is 7 cm shorter than the other leg. Its area is 30cm^2. Find its perimeter.

Solution :

Let X = length of one leg

X + 7 = length of the other leg

Area of a triangle = (bh)/2

Working Equation :

X (X+7)/2 = 30

(X(X+7)/2 = 30) 2

X^2 + 7X = 60

X^2 + 7X - 60 = 0

Factoring X^2 + 7X -60

(X -5 ) ( X + 12 ) = 0

X – 5 = 0 therefore X = 5

Leg1 = 5

Leg2 = 5 + 7 = 12

Finding the hypotenuse:

Hypotenuse = SQRT(5^2 + 12^2) = SQRT(25 + 144) = SQRT (169) =13

Perimeter = 5+12+13 = 30 vcentimeters.

Problem Number Three :

One side of a triangle is one dm. less than its diagonal. If the perimeter of the rectangle is 62, find the area of the rectangle.

Solution :

Length of the rectangle = d – 1

To represent width use phytagorean theorem and consider diagonal as hypotenuse:

d^2 = w^2 + (d – 1)^2

Rearranging the equation : w^2 = d^2 - (d-1)^2

w^2 = d^2 –d^2 +2d – 1

w^2 = 2d -1

w = SQRT(2d -1)

Working Equation : Based from Perimeter = 2l + 2W

2(d-1) + 2 SQRT(2d- 1 ) = 62

2d – 2 + 2 SQRT(2d-1) = 62

(2SQRT(2d -1 ) = 64 -2d) ½

SQRT(2d – 1) = 32 – d

(SQRT(2d -1 ))^2 = (32 –d)^2

2d -1 = 1024 -64d + d^2

d^2 - 66d + 1025 = 0

Factoring gives (d – 41) (d -25) = 0

d – 25 = 0

d = 25

Length = d – 1 = 25 – 1 = 24

Width = SQRT(2d-1) =SQRT(50- 1) = SQRT49 = 7

Area of the rectangle = (24)(7) = 168 dm^2


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    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      4 years ago from Manila

      Thanks for dropping by. God bless you.

    • profile image


      4 years ago

      thank you for so much for this site

    • profile image


      4 years ago

      tnx for this site

    • profile image


      5 years ago

      tnx for the problems and solution

    • profile image

      Jaspher Bauttista 

      5 years ago

      Tnx For the Problems Now i know how toooo

    • profile image


      6 years ago

      can you please tell me if what is 5 main problems invoving quadratic equations?

    • profile image

      ian relacion 

      6 years ago

      ohhhhhhhhh that's cool i can make my assignment now

    • profile image

      frederick vidad 

      6 years ago

      tnx for this site

    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      7 years ago from Manila

      Hi skye2day it is great to hear from you again. I am glad that you appreciated this Mathematics hub. I believe God is also the God and creator of Mathematics and number systems. In the Bible there are also numbers and measurements. I always find Mathematics an interesting subject and I enjoy doing its workings.It is my main source of bread and butter. Thank you for paying a visit to this hub. Your presence here is a great source of encouragement. May you be blessed today and always. Best regards.

    • skye2day profile image


      7 years ago from Rocky Mountains

      OH drat I lost the first comment. The enemy can take a hike to the pits where he is the name above all names Jesus Christ.

      This really got me to thinking about how our Lord GOD in all His creation came up with the 10 numbers that have a huge huge massive impact in each area of our life. Gods mind is omnipresent He is so amazing.

      I think if you were my math teacher i may have understood a whole lot more. I just did not get math. Now today when I study scripture I see Gods creation of numbers in a spiritual manner and how finite my mind really is. This is really a thought provoking hub for me. Have you given thought to Gods number system and how massive it has been in all of time?

      I am sure you have you since you are a teacher of math. That is amazing. Well sister so nice to visit you. I do lift you in prayer and hope all is well with you and yours. You keep on in the Light sis. You will I kinow it Phil 4:13. I just love ya, you are precious. Gods Blessings always and 4 ever sista. In Christ.

    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      7 years ago from Manila

      Hi Dylesten and reymac thank you for taking time to visit this hub. Blessings to you always and regards.

    • profile image


      7 years ago

      Thank you for giving this website because it gives a better future for the students and children work hard for math.....'''''''';;;;Thank you very much'''''''''''.......

    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      7 years ago from Manila

      Hi ronhi thank you for visiting this hub. Blessings to you and regards.

    • ronhi profile image


      7 years ago from Kenya

      You must be a really good maths teacher:-)


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