Question

diffrence of perimeter of two squares is 32m and difference oof their areas is 208sqcm
find the difference of their sides ​

Answer 1

Answer:

The difference between the sides of the two squares is 8 cm.

Step-by-step-explanation:

Let the side of the bigger square be x cm.

And the side of the smaller square be y cm.

We know that,

Perimeter of square = 4 * Side

∴ Perimeter of bigger square = 4x cm

Perimeter of smaller square = 4y cm

From the first condition,

Perimeter of bigger square - Perimeter of smaller square = 32 cm

⇒ 4x - 4y = 32

⇒ 4 ( x - y ) = 32

⇒ x - y = 32 ÷ 4

⇒ x - y = 8

⇒ x = 8 + y

⇒ x = y + 8 - - - ( 1 )

Now, we know that,

Area of square = ( Side )²

∴ Area of bigger square = x² sq.cm

Area of smaller square = y² sq.cm

From the second condition,

Area of bigger square - Area of smaller square = 208 sq.cm

⇒ x² - y² = 208

⇒ ( x + y ) ( x - y ) = 208

⇒ ( y + 8 + y ) ( y + 8 - y ) = 208 - - - [ From ( 1 ) ]

⇒ ( y + y + 8 ) ( y - y + 8 ) = 208

⇒ ( 2y + 8 ) * 8 = 208

⇒ 2y + 8 = 208 ÷ 8

⇒ 2y + 8 = 26

⇒ 2y = 26 - 8

⇒ 2y = 18

⇒ y = 18 ÷ 2

⇒ y = 9

∴ Side of smaller square = 9 cm

By substituting y = 9 in equation ( 1 ), we get,

x = y + 8 - - - ( 1 )

⇒ x = 9 + 8

⇒ x = 17

∴ Side of bigger square = 17 cm

Now, we have to find difference between the sides,

∴ Difference = Side of bigger square - Side of smaller square

⇒ Difference = 17 - 9

⇒ Difference = 8 cm

∴ The difference between the sides of the two squares is 8 cm.