Question

Sum of the areas of two squares is 400 cm². If the difference of their
perimeters is 16 cm, find the sides of the two squares. (CBSE 2013]

Answer 1

Answer:

16,12

Step-by-step explanation:

side of 1st square be x and 2nd be y

area = x², perimeter= 4x

sum of squares = x²+y²=400 -----(1)

difference in perimeter 4x-4y= 16

x-y = 4

x=4+y ----(2)

sub (2) in (1)

y²+ (4+y)²=400

y²+ 16+y²+8y=400

2y²+8y-384=0. (divide by 2)

y²+4y-192=0

y²+16y-12y-192=0

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

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

y= 12, y= -16 (since length is not negative )

so length side is y= 12

another side is x= y+4= 16