Question

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

Answer 1

Answer:

Ratio in length and breadth of a rectangular piece of land = 5 : 3

Cost of fencing = ₹ 9600

And rate = ₹ 24 per m

Perimeter = Total cost of fencing/Rate per m = 9600/24 = 400 m

Let length = 5x

Then breadth = 3x

∴ Perimeter = 2(l + b)

400 = 2 × (5x + 3x)

∴ 16x = 400

x = 400/16 = 25

(i) ∴ Length of land = 5x = 5 × 25 = 125 m

And breadth = 3x = 3 × 25 = 75 m

(ii) Area = l × b

= 125 × 75 = 9375 m2

(iii) Cost of levelling at rate ₹ 60 per m2

= ₹ 60 × 9375 m2 = ₹ 5, 62,500

Answer 2

$\huge\rm\underline\purple{Question :-}$

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

$\huge{\underbrace{\textsf{\textbf{\color{lightpink}{Solution :-}}}}}$

$\huge{\bold{\color{navy}{Given,}}}$

Ratio in length and breadth of a rectangular piece of land = 5 : 3

Cost of fencing = ₹ 9600

And rate = ₹ 24 per m

$\red{\underline\bold{To\:find,}}$

• Length = ?
• Breadth = ?

$\orange{\underline\bold{We\: know\: that,}}$

Perimeter = $\frac{Total \:cost\: of\: fencing}{Rate\: per\: m}$

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

Let length = 5x

Then breadth = 3x

$\green{\underline\bold{By\: using\: Formula}}$

∴ Perimeter = 2(l + b)

400 = 2 × (5x + 3x)

∴ 16x = 400

x = $\frac{400}{16}$ = 25

∴ Length of land = 5x = 5 × 25 = 125 m

And breadth = 3x = 3 × 25 = 75 m