Question

The sum of the areas of two squares is 400 sq.m. If the difference
between their perimeters is 16 m, find the sides of two squares.
​

Answer 1

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Answer 2

The sides of squares are 16 cm and 12 cm

Step-by-step explanation:

let the side of one square be x

and side of another square be y

therefore according to question

x²+y²=400..(1)

4x-4y=16..(2)

x-y=4

x= 4+y..(3)

put the value of x in equation 1

we get

(4+y)²+y²=400

4²+y²+8y+y²=400

2y²+8y=400-16

2y²+8y- 384=0

y²+4y-192=0

y²-12y-16y-192=0

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

(y+16) (y-12)

y +16=0

y=-16 (neglected )

y-12=0

y=12

then x= 4+y = 4+12=16

x=16

hence the sides of squares are 16 cm and 12 cm

#Learn more:

The sum of the areas of two squares is 274 sq.m. If the difference of

their perimeters is 32 m, find the sides of the two squares.​

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