Question

Perimeter of a rectangle is equal to the perimeter of square whose area is 324 cm^2.Find the area of rectangle if length of rectangle is 6 more than the side of square?

Answer 1

Answer:

Area of square=324 cm^2

But area of square=s*s (s=side)

s*s=324 cm^2

s=✓324

s=18

Let the length of rectangle be l

As per question

l=6+18

l=24

Perimeter of rectangle= perimeter of square (given)

2(l+w)=4s, where w is the width of rectangle

2(24+w)=4*18

48+2w=72

2w=24

w=12

Area of rectangle=l*w

Area =24*12

Area=288 cm^2

Answer 2

✬ Area = 288 cm² ✬

Step-by-step explanation:

Given:

• Perimeter of rectangle is equal to perimeter of square.
• Area of square is 324 cm².
• Length of rectangle is 6 more than side of square.

To Find:

• What is the area of rectangle ?

Solution: Let the side of square be s cm and breadth of rectangle be b cm. Therefore,

➯ Length of rectangle = (6 more than s)

➯ Length of rectangle = ( 6 + s )

So, Perimeter of rectangle will be

➮ 2(Length + Breadth)

➮ 2(6 + s + b)...............(1)

As we know that

★ Area of Square = (Side)²

$\implies{\rm }$ 324 = (s)²

$\implies{\rm }$ √324 = s

$\implies{\rm }$ √18 $\times$ 18 = s

$\implies{\rm }$ 18 cm = side

So, the side of square is 18 cm. So length of Rectangle is (6 + side) = 6+18 = 24 cm

★ Perimeter of Square = 4 $\times$ Side ★

➨ Perimeter = 4 $\times$ 18

➨ Perimeter = 72 cm...........(2)

A/q

• Equation 1 = Equation 2

$\implies{\rm }$ 2( 6 + s + b ) = 72

$\implies{\rm }$ 2 ( 6 + 18 + b ) = 72

$\implies{\rm }$ 2 ( 24 + b ) = 72

$\implies{\rm }$ 48 + 2b = 72

$\implies{\rm }$ 2b = 72 – 48

$\implies{\rm }$ 2b = 24

$\implies{\rm }$ b = 24/2

$\implies{\rm }$ b = 12 cm

∴ Breadth of rectangle is 12 cm. Now

★ Area of Rectangle = (Length)(Breadth) ★

➟ Area = (24 $\times$ 12)

➟ Area = 288 cm²

Hence, Area of Rectangle is 288 cm².