Question

Sum of the areas of two squares is 157 m². If the sum of their perimeters is 68 m, find the sides of the two squares.

The sum of the areas of two squares is 157 m². If the sum of their perimeters is 68 m, find the sides of the two squares.

Answer 1

Let the side of one square be x

And a side of other square be y

Sum of an area of two square is 157

Equation becomes

x² + y² = 157   ...(1)   (∵ Area of square is side²)

Now, sum of their perimeters is 68

Equation becomes

4x + 4y = 68   ...(∵ Perimeter of square is 4 × side)

Solving the two-equation by substitution method

4x + 4y = 68

x + y = 17

⇒ x = 17 – y   ...(2)

Substitute (2) in (1)

(17 – y)² + y² = 157

289 + y² – 34y + y² = 157

2y² – 34y + 132 = 0

y² – 17y + 66 = 0

Using `y = (-b ± sqrt(b^2 - 4ac))/(2a)`

Plugging the values in the formula we get

`y = (17 ± sqrt(289 - 4(66)))/2`

`y = (17 ± sqrt(25))/2`

`y = (17 ± 5)/2`

`y = 12/2, 22/2`

y = 6, 11

When y = 6 then x = 11

And when y = 11 then x = 6

Therefore, the sides of square are 6 m and 11 m.