Question

The perimeter of a rectangle is 54cm.if its width is 2 cm more than one fourth of its lenght then lenght is

Answer 1

Answer:

Length of a rectangle is 20 cm

Step-by-step explanation:

Given :

• The perimeter of a rectangle is 54 cm

• Width is 2 cm more than one fourth of its length

Find :

• Length of a rectangle

Solution :

Let,

Length of a rectangle = x

Width of a rectangle = 1/4 x + 2

(0.25x + 2)

1/4 = 0.25

So,

Perimeter of rectangle = 2 (length + width)

➨ 2 (x + 0.25x + 2) = 54

➨ 2x + 0.5x + 4 = 54

➨ 2.5x = 54 - 4

➨ 2.5x = 50

➨ x = 50 / 2.5

➨ x = 20

Therefore,

Length of a rectangle is 20 cm

★ Verification :

Width of a rectangle = 1/4 x + 2

➨ 20 / 4 + 2

➨ 5 + 2

➨ 7

★ Perimeter of rectangle = 2 (length + width)

➨ 2 ( 20 + 7)

➨ 2 (27)

➨ 54

Answer 2

Let us take length as $x$ and width as  $\frac{1}{4} x+2$ .

Perimeter of the rectangle = 54 cm

Perimeter = 2 ( length + width )

$\longrightarrow 2( x +\frac{1}{4} x + 2) = 54$

$\longrightarrow x+\frac{1}{4} x+2 = 27$

$\longrightarrow x +\frac{1}{4}x = 25$

$\longrightarrow\frac{4x+x}{4} = 25$

$\longrightarrow 5x = 100$

$\longrightarrow \underline { x = 20}$

Breadth = $\frac{20}{4} +2$

            = $5+2$

            = $7 cm$

Length = $20 cm$

HOPE IT HELPS U ............