Question

The length and breadth of a rectangular lawn are in the ratio 5:3. If the area of the lawn is 3375 m2
and the cost of fencing the lawn is ₹ 8.50 per metre. ANSWER THE FOLLOWING QUESTIONS
i. Find the length of the rectangular lawn
a. 75 m b. 105 m c. 30 m d. 35 m
ii. Find the breadth of the lawn
a. 80 m b. 75 m c. 45 m d. 15 m
iii. Find the perimeter of the rectangular lawn
a. 225 m b. 240 m c. 380 m d. 720 m
iv. Find the total cost of fencing the lawn
a. Rs 5060 b. Rs 4020 c. Rs 4050 d. Rs 2040

Answer 1

Step-by-step explanation:

As per the provided information in the given question, we have :

• The length and breadth of a rectangular lawn are in the ratio 5:3.
• Area of the lawn = 3375 m²
• Cost of fencing per m = ₹ 8.50

Assumption : Let us say that, length of the lawn is 5x and breadth of the lawn is 3x.

$\sf 3x \: \: \huge\boxed{\begin{array}{cc} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{array}} \\ \: \: \: \: \: \: \: \sf 5x \: m$

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

I. Find the length of the rectangular lawn :

We have,

• Length = 5x
• Breadth = 3x

As we know that,

$\longrightarrow \sf{\quad {A_{(Rectangle)} = Length \times Breadth }}$

Substitute the values.

$\longrightarrow \sf{\quad {3375= 5x \times 3x }}$

Performing multiplication.

$\longrightarrow \sf{\quad {3375= 15x^2}}$

Transposing 15 from RHS to LHS.

$\longrightarrow \sf{\quad {\cancel{\dfrac{3375}{15}}= x^2}}$

Dividing 3375 by 15.

$\longrightarrow \sf{\quad {225= x^2}}$

Now, balancing the equation.

$\longrightarrow \sf{\quad {\sqrt{225}= x}}$

Square root of 225 is 15.

$\longrightarrow \sf{\quad {15 = x}}$

Now,

↠ Length = 5x = 5(15) = 75 m (Option A)

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

ii. Find the breadth of the lawn

↠ Breadth = 3x = 3(15) = 45 m

(Option C)

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

iii. Find the perimeter of the rectangular lawn

$\longrightarrow \sf{\quad { P_{(Rectangle) }= 2(\ell + b)}}$

Substitute the values.

$\longrightarrow \sf{\quad { P_{(Rectangle) }= 2(75 \; m+ 45 \; m)}}$

Performing addition in the brackets.

$\longrightarrow \sf{\quad { P_{(Rectangle) }= 2(120 \; m)}}$

Performing multiplication..

$\longrightarrow \bf{\quad { P_{(Rectangle) }= 240 \; m}}$

(Option B)

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iv. Find the total cost of fencing the lawn

↠ Total cost of fencing = Perimeter × Cost of fencing per m

↠ Total cost of fencing = Rs. (240 × 8.50)

↠ Total cost of fencing = Rs. 2040

(Option D)

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