Question

the sum of perimeter of a rectangle of sides 35cm and 24cm, is equal to the perimeter of a square l. Find the side and area of the square​

Answer 1

✬ Area = 870.25 cm² ✬

Step-by-step explanation:

Given:

• Perimeter of rectangle is equal to the perimeter of square.
• Measure of length and breadth of rectangle is 35 & 24 cm.

To Find:

• What is the side and area of the square ?

Solution: As we know that formula for finding perimeter of rectangle is

★ Perimeter of Rectangle = 2 ( Length + Breadth ) ★

• Length = 35 cm
• Breadth = 24 cm

$\implies{\rm }$ Perimeter = 2 ( 35 + 24 )

$\implies{\rm }$ Perimeter = 2 $\times$ 59

$\implies{\rm }$ Perimeter = 118 cm

So, Perimeter of rectangle is 118 cm.

Now, Let the meaure of each side of Square be S cm. Therefore,

★ Perimeter of Square = 4 (Side) ★

$\implies{\rm }$ Perimeter = 4S

So, Perimeter of square is 4S.

According to the question:-

• Perimeter rect. = Perimeter sq.

➽ 118 = 4S

➽ 118/4 = Side

➽ 29.5 cm = Side of square

∴ Area of Square = (Side)²

➬ Area = (29.5)² cm²

➬ Area = ( 29.5 $\times$ 29.5 ) cm²

➬ Area = 870.25 cm²

Hence, the area of square is 870.25 cm².

Answer 2

Given:

Sides of the rectangle are

length = 35 cm

breadth = 24 cm

To be found:

Sides of square and Area of square

According to questions,

the sum of the perimeter of a rectangle is equal to the perimeter of a square.

Now,

Perimeter of rectangle = 2(l+b) units

[ ∵ Here 'l' is 'length' and 'b' is 'breadth' ]

So,

perimeter of rectangle

= 2(35 + 24)

= 2(59)

= 118 cm

Also, the perimeter of the square is 118 cm (ATQ).

So,

→ 4 × (side) = 118

→ side = 118 ÷ 4

→ side = 29.5 cm

$\rule{200}2$

Now, the area of the square

= (side)²

= (29.5)²

= 29.5 × 29.5

= 870.25 cm²

∴ Side of square = 29.5 cm

And

Area of square = 870.25 cm²