Finding Length and Perimeter of a Rectangular Compound

MathematicsMensurationEasy

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9. Fencing a rectangular compound of a house cost ₹5432. If the rate of fencing is ₹94 per metre, find the perimeter of the compound. If the breadth of the compound is $10 \text{ m}$, find its length.

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1
Step 1

Let's solve this problem about fencing a rectangular compound. We are given the total cost, the rate per metre, and the breadth of the compound.

Problem Analysis

Total Cost = ₹ 5432

Rate = ₹ 94/m

Breadth ($b$) = 10 m

2
Step 2

First, we need to find the perimeter of the compound. We know that the total cost of fencing is equal to the perimeter multiplied by the rate.

$$\text{Total Cost} = \text{Perimeter} \times \text{Rate}$$
3
Step 3

So, to get the perimeter, we divide the total cost by the rate of fencing.

4
Step 4

Plugging in our values, we have five thousand four hundred and thirty-two divided by ninety-four.

$$\text{Perimeter} = \frac{5432}{94}$$
5
Step 5

Calculating this division gives us fifty-eight. So the perimeter of the compound is fifty-eight metres.

6
Step 6

Now that we have the perimeter and we know the breadth is ten metres, we can find the length.

Finding the Length

$$P = 58\text{ m}$$
$$b = 10\text{ m}$$

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About This Question

Subject
Mathematics
Topic
Mensuration
Difficulty
Easy
Question Type
Open Ended

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