# The Sum of the Areas of Two Squares is 640m^2 . If the Difference in Their Perimeter Be 64m, Find the Sides of the Two Square - Mathematics

The sum of the areas of two squares is 640m^2 . If the difference in their perimeter be 64m, find the sides of the two square

#### Solution

Let the length of the side of the first and the second square be x and y. respectively. According to the question:

x^2+y^2=640                                 ................(1)

Also,

4x-4y=64

⇒x-y=16

⇒x=16+y

Putting the value of x in (1), we get:

x^2+y^2=640

⇒(16+y)^2+y^2=640

⇒256+32y+y^2+y^2=640

⇒2y^2+32y-384=0

⇒y^2+16y-192=0

⇒y^2+(24-8)y-192=0

⇒y^2+24y-8y-192=0

⇒y(y+24)-8(y+24)=0

⇒(y+24)(y-8)=0

⇒y=-24  or  y=8

∴ y=8                                    (∵ Side cannot be negativ)

∴ x=16+y=16+8=24m

Thus, the sides of the squares are 8 m and 24 m.

Is there an error in this question or solution?
Chapter 10: Quadratic Equations - Exercises 5

#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths