Question

Sum of the areas of two squares is 157 m^2 . If the sum of their perimeters is 68 m , find the sides of the two squares

Answer 1

here's your answer

hope this is clear

Answer 2

Answer:

11 and 6

Step-by-step explanation:

Let the sides of the two squares be x and y.

Their areas will be :

x² and y² respectively.

Now their perimeters will be :

4x and 4y respectively.

We do this since the sides of a square are equal.

From the question we can do the substitution as follows:

Sum of the areas:

x² + y² = 157...........1)

4x + 4y = 68......2)

Divide equation 2 all through by 4 to get :

x + y = 17

We need to solve for x and y.

By substitution we have :

x = 17 - y

Replace this in equation 1 as follows:

(17 - y)² + y ² = 157

289 - 34y + y² + y² = 157

Collecting the like terms together we have :

2y² - 34y + 132 = 0

Solving the quadratic equation:

Divide through by 2 to get :

y² - 17y + 66 = 0

The roots are :

-11 and -6

We expand the equation as follows:

y² - 11y - 6y + 66 = 0

y(y  - 11) - 6(y - 11) = 0

(y - 6)(y - 11) = 0

y = 6 or 11

When y is 11 x is (17 - 11) = 6

So the values can either be 6 or 11 for y or vice versa for x.

The sides are thus :

11 meters and 6 meters