Question

The combined area of two squares is 45 cms. each side of one square is twice as long as a side of the other square

Answer 1

Answer:

${ \bold{ \red{Given}}}$

• Combined area of two squares is 45 cms
• Each side of one square is twice as long as a side of the other square

${ \bold{ \pink{Find}}}$

• Length of each side of the larger square

${ \bold{ \green{Solution}}}$

Let take the side of first square as x,

We know, that

${ \boxed{area \: of \: square = {s}^{2} }}$

Area of first square = x×x = x²

Let take the side of larger square as 2x ,

Area of Larger square = 2x × 2x = 4x²

From question, the combined area two squares is 45cm:-

${ \to{ \sf \: { {x}^{2} + 4{x}^{2} = 45}}}$

${ \to{ \sf{5 {x}^{2} = 45}}}$

${ \to{ \sf{ {x}^{2} = \frac{45}{5} }}}$

${ \to{ \sf{ {x}^{2} = 9}}}$

${ \to{ \sf{x = \sqrt{9} }}}$

${ \to{ \sf{x = 3}}}$

Side of second sqaure = 2x = 2 × 3 = 6

"Therefore, Length of large square is 6."

Answer 2

Given: Combined area of two squares = 45 cm²

           Side of one square is twice the side of another square

To find: Length of side of each square

Solution: Let the side of one square be x cm.

Therefore, the side of another square = 2x cm

According to the question,

x² + (2x)² = 45

⇒ x² + 4x² = 45

⇒ 5x² = 45

⇒ x² = 9

⇒ x = ±3

Since the side of a square cannot be negative, we consider x = 3.

Hence, side of one square = 3 cm.

The side of another square = 2 × 3 cm = 6 cm

Answer: 3 cm, 6 cm