Question

The perimeter of rectangle is half of 108cm. It's breadth is 7cm less than its length. Find the dimensions of the rectangle.

Answer 1

Step-by-step explanation:

given perimeter of the rectangle= 1/2of 108=54

and the breadth is 7cm less than length

let the length be =X

breadth=x-7

perimeter of the rectangle=2(l+b)

2(X+x-7) =54

2x+2x-14=54

4x-14=54

4x=54+14

4x=68

X=68/4

X=17

length=17

breadth=17-7=10

Answer 2

Answer :

The dimensions of the rectangle :

length is 17cm and breadth is 10cm

Given :

• The perimeter of a rectangle is half of 108cm
• Its breadth is 7cm less than its length

To Find :

• The dimensions of the rectangle.

Formula to be used :

If l and b are respectively the length and breadth of a rectangle then its perimeter is given by :

$\sf \star \: \: Perimeter \: of \: rectangle = 2 (l + b)$

Solution :

Let us consider the length and breadth of the rectangle be x and y respectively.

According to question

$\sf \implies 2 (x + y) = \dfrac{1}{2}\times 108 \\\\ \sf \implies 2 (x + y) = 54 \\\\ \sf \implies x + y = \dfrac{54}{2} \\\\ \sf \implies x + y = 27 \\\\ \sf \implies y = 27 - x .......(1)$

Again by question

$\sf \implies y = x - 7 ........ (2)$

Comparing (1) and (2) we have :

$\sf\implies x-7 = 27 -x \\\\ \sf \implies x + x = 27 + 7 \\\\ \sf \implies 2x = 34 \\\\ \sf \implies x = \dfrac{34}{2} \\\\ \sf \implies x = 17cm$

Using the value of x in (1) we have : $\sf \implies y = 27 - 17 \\\\ \sf \implies y = 10 cm$

Thus the dimensions are :

length = 17cm

breadth = 10cm