Question

The length and breadth of rectangular garden is in the ratio 4:3. If the area is 7500 m^2 , find the cost of fencing the garden at the rate of 6 rupees per metre

Answer 1

Answer:

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Answer 2

Given

• Length and Breadth = 4:3
• Area = 7500 m²
• Rate of Fencing = ₹6 per m

Explanation

Let the Length and Breadth of the Rectangular garden be 4x and 3x Respectively.

✮We know that:

$\maltese {\pmb{\boxed{\sf{ Area_{(Rectangle)} = l \times b }}}} \\ \\ \\ \colon\implies{\sf{ 7500 = 4x \times 3x }} \\ \\ \\ \colon\implies{\sf{ 7500 = 12x^2 }} \\ \\ \\ \colon\implies{\sf{ \cancel{ \dfrac{7500}{12} } = x^2 }} \\ \\ \\ \colon\implies{\sf{ 625 = x^2 }} \\ \\ \\ \colon\implies{\sf{ \sqrt{625} = x }} \\ \\ \\ \colon\implies{\sf{ x = 25 }}$

Therefore,

• Length = 4x = 4×25= 100 metres
• Breadth = 3x = 3×25 = 75 metres

✮Now, We can find Perimeter of the Rectangular garden to find cost of Fencing :-

$\maltese {\pmb{\boxed{\sf{ Perimeter_{(Rectangle)} = 2(l+b) }}}} \\ \\ \\ \colon\implies{\sf{ Perimeter_{(Rectangle)} = 2(100+75) }} \\ \\ \\ \colon\implies{\sf{ Perimeter_{(Rectangle)} = 2(175) }} \\ \\ \\ \colon\implies{\sf\blue{ Perimeter_{(Rectangle)} = 350 \ Metres }}$

Since, Perimeter of Garden is 350 Metres.

✮At the Rate of cost of Fencing is ₹6 per m :-

$\colon\mapsto{\sf{ 6 \times 350 }} \\ \\ \colon\mapsto{\sf{ Rs. \ 2100 }}$

Hence,

${\underline{\sf{ The \ Cost \ Fencing \ the \ Rectangular \ garden \ will \ be \ Rs. \ 2100 .}}}$