Question

The sum of the areas of two square is 41q cm. If the sum of their perimeter is 36 cm then find the side of two square​

Answer 1

Given,

• The sum of the areas of two square is 41cm².
• The sum of their perimeter is 36 cm.

To Find,

• Find the side of two square.

Solution,

Let's

The Side Of First Square = X

The Side Of Second Square = Y

The Area Of First Square

→ (Side)²

→ X²

The Area Of Second Square

→ (Side)²

→ Y²

The Perimeter of First Square

→ 4(Side)

→ 4(X)

→ 4X

The Perimeter of Second Square

→ 4(Side)

→ 4(Y)

→ 4Y

Sum of The Areas = 41cm²

→ X² + Y² = 41cm²

Sum of the Perimeters = 36cm

→ 4X + 4Y = 36cm

→ 4(X + Y) = 36cm

→ X + Y = 9cm

X² + Y² = 41 •••(1st)

X + Y = 9 •••(2nd)

Finding The Value of Y in 2nd Equation;

X + Y = 9 •••(2nd)

Y = 9 - X •••(3rd)

Substituting the Value Of Y in 1st Equation;

X² + Y² = 41 •••(1st)

→ X² + (9 - X)² = 41

→ X² + 81 - 2(9)(X) + X² = 41

→ X² + X² + 81 - 41 - 18X = 0

→ 2X² - 18X + 40 = 0

→ 2(X² - 9X + 20) = 0

→ X² - 9X + 20 = 0/2

→ X² - 9X + 20 = 0

→ X² - 5X - 4X + 20 = 0

→ X(X - 5) - 4(X - 20) = 0

→ (X - 4)(X - 5) = 0

X - 4 = 0

X = 4

Substituting the Value Of X in 2nd Equation;

Y = 9 - X •••(3rd)

Y = 9 - X

Y = 5

Required Answer,

Sides Are 4cm And 5cm.