Question

Perimeter of a rectangle is 500 cm. If the
breadth is one-fourth of its length. Find the
dimensions of the rectangle,​

Answer 1

Let length of the rectangle = L

breadth B = L/4

Perimeter = 500 cm

Perimeter of a rectangle = 2(length + breadth)

500 = 2(L + L/4)

500 = 4L + L

2 4

250 = 5L

4

250 × 4 = 5L

1000 = 5L

L = 1000

5

L = 200

B = 200/4 = 50

Length of rectangle = 200 cm

Breadth of rectangle = 50 cm

Answer 2

${\large{\mathfrak{\blue{\underline{\red{Solution:}}}}}}$

Let,

• The length of rectangle be x
• The breadth of rectangle be $\dfrac{x}{4}$

Now,

We know that,

${\green{\boxed{\sf{Perimeter\;of\;Rectangle= 2 ( l + b) }}}}$

So,

$\pink{\rightarrow}$ Perimeter = 2 ( l + b )

$\pink{\rightarrow}$500 = 2 ( x + $\dfrac{x}{4}$ )

$\pink{\rightarrow}$ 500 = 2 × $\dfrac{4x + x}{4}$

$\pink{\rightarrow}$500 = 2 × $\dfrac{5x}{4}$

$\pink{\rightarrow}$500 = $\dfrac{5x}{2}$

$\pink{\rightarrow}$500 ×$\dfrac{2}{5}$ = x

$\pink{\rightarrow}$100 × 2 = x

$\pink{\rightarrow}$200 = x

Now,

$\sf{\purple{Length}}$ = x = 200 cm

$\sf{\purple{Breadth}}$ = $\dfrac{x}{4}$ = $\dfrac{200}{4}$ = 50 cm

Therefore, the dimensions of rectangle are 200 cm and 50 cm.