Question

The length and breadth of a rectangular piece of land are in the ratio of 5:3.lf the total cost of fencing it at ₹ 24 per metre is ₹ 9600, find its length and breadth.

Answer 1

let the length and breadth be

5x and 3x

perimeter=9600/24
=400

P=2(l+b)
400=2(5x+3x)
400=2×8x
400=16x
400/16=x
25=x

length is 125 metre and breadth is 75m

Answer 2

let the common factor be x

length = 5x
breadth = 3x

Perimeter of the piece of land

$\frac{9600}{24} m$
= 400 m

perimeter = 2 ( l + b )
400 = 2 ( 5x + 3x )
400/2 = 8x
200 = 8x

$x = \frac{200}{8}$
x = 25

length = 5x = 5 × 25 = 125m
breadth = 3x = 3 × 25 = 75m

Alternative,

let the common factor be x

length = 5x
breadth = 3x

Perimeter = 2 ( l + b )
= 2 ( 5x + 3x )
= 2 × 8x
= 16x

here , an equation will be formed,

$16x \times 24 = 9600$
$16x = \frac{9600}{24}$
$16x = 400$
$x = \frac{400}{16}$
x = 25

length = 5 × 25 = 125m
breadth = 3 × 25 = 75m

Hope helped.