Question

8. The length and breadth of a rectangular piece of land ace 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

• The length and the breadth will be 125 m & 75 m

Explanation

Given

• Length and the breadth of a rectangle are of the ratio 5:3
• Cost of fencing is ₹24 per m
• Total cost = 9000

To Find

• Length & Breadth of the rectangle

Solution

Let,

• Length = 5x
• Breadth = 3x

✭ Perimeter

→ Perimeter = Total Cost/Cost per m

→ Perimeter = 9000/24

→ Perimeter = 400 m

✭ Finding x

→ Perimeter = 2(l+b)

→ 400 = 2(5x+3x)

→ 400/2 = 8x

→ 200 = 8x

→ 200/8 = x

→ x = 25

✭ Length and Breadth

→ Length = 5x = 5×25 = 125 m

→ Breadth = 3x = 3×25 = 75 m

Answer 2

Question:-

The length and breadth of a rectangular piece of land ace 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:-

• The length is 125 m
• The breadth is 75 m

Solution:-

• Ratio of length and breadth = 5:3

Put x in the ratio

• Length = 5x
• Breadth = 3x

• Total cost of fencing = ₹9600
• Cost of fencing (per m) = ₹24

$\green{ \large{perimeter = \frac{total \: cost}{cost \: (per \: m)} }}$

$\large{\tt:\implies\: \: \: \: \: \: \: \: {}perimeter = \frac{9600}{24} }$

$\large{\tt:\implies\: \: \: \: \: \: \: \: {}perimeter = 400 \: m}$

• The perimeter of the land is 400 m.

$\red{ \boxed{ \large{ \blue{perimeter = 2(l + b)}}}}$

$\large{\tt:\implies\: \: \: \: \: \: \: \: {}2(5x + 3x) = 400}$

$\large{\tt:\implies\: \: \: \: \: \: \: \: {}5x + 3x = \frac{400}{2} }$

$\large{\tt:\implies\: \: \: \: \: \: \: \: {}8x = 200}$

$\large{\tt:\implies\: \: \: \: \: \: \: \: {}x = \frac{200}{8} }$

$\large{\tt:\implies\: \: \: \: \: \: \: \: {}x = 25}$

• The value of x is 25 m.

___________________________

• Length = 5x = 5×25 = 125 m
• Breadth = 3x = 3×25 = 75 m

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