Question

The sum of the areas of two squares is 400 square cm if the difference of their perimeter is 16cm find sides of two squares

Answer 1

Let the two sides of square be x and y

According to the question

x² + y² = 400 -(1)

4x-4y =16

4(x-y) =16

x-y=4

x=y+4

now putting the value of x in equation (1)

(y+4)²+ y²=400

y²+16+8y+y²=400

2y²+8y+16-400=0

2y²+8y-384=0

2(y²+4y-192)=0

y²+4y-192=0/2

y²+4y-192=0

y²+16y-12y-192=0

y(y+16)-12(y+16)

(y-12) (y+16)=0

y=12 or y=-16(not possible b'coz length cannot be negative)

y=12

putting value of y in equation 2

x-y=4

x-(+12)=4

x=16