Question

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

Answer 1

Let the side of one square be x and second be y.

We know that perimeter of square = 4 * side

= 4x and 4y

It is Given that the difference of their perimeters is 16.

So, 

4x - 4y = 16

=> x - y = 4

=> x = 4 + y        ...........(i)

Also, area of two triangles :

= x² and y²                 {because area = side²}

It is given that the sum of area of the two squares is 400.

So, 

x² + y² = 400

From (i), we get x = y+4.

Putting,

(y+4)² + y² = 400

y² + 8y + 16 + y² = 400.

2y² + 8y - 384 = 0

y² + 4y - 192 = 0.

y²-12y+16y-192=0

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

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

y+16=0      or  y-12=0

y= -16  or        y=12.

As a side can't be negative. So, the side of the square is 12 cm.

And the Side of second one = y+4 = 16 cm.