Question

The width of a rectangle is half the length. the perimeter of the rectangle is 54 in. what is the length of the rectangle?​

Answer 1

GIVEN:

• Width of rectangle is half of length
• Perimeter of rectangle=54 in.

TO FIND:

• Length of rectangle

SOLUTION:

Let length of rectangle be 2x.

$\sf Then \: width \: will \: be \: \frac{1}{2} \times 2x$

Width=x

As we know that formula to find perimeter of rectangle is:-

2(L+B)

[Where L is length and B is breadth)

$\sf : \implies \: \: 2(2x + x) = 54 \: in$

$\sf : \implies \: \: 4x + 2x = 54 \: in$

$\sf : \implies \: \: 6x = 54 \: in$

$\sf : \implies \: \: x = \frac{54}{6} \: in$

$\sf : \implies \: \: x = 9 \: in$

Our assumption is:-

Length of rectangle is 2x=>2×9

So length of rectangle is 18 cm.

More formulae to know!

• Area of rectangle=Length×width
• Perimeter of square=4×side
• Area of square=side²

Answer 2

Given :

• The width of a rectangle is half the length.
• The perimeter of the rectangle is 54 cm.

To find :

• The length of the rectangle

Solution :

★ Let:-

• Width = x
• Length = 2x

★ We know:-

• Perimeter = 2(length + breadth)

→ 54 = 2(2x + x)

→ 54 = 4x + 2x

→ 54 = 6x

→ 54/6 = x

→ x = 9

•°• the length = 2x = 18

Answer :

• The length of the rectangle is 18 cm