Question
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c) The area of a rectangle is \( 70 \mathrm{~cm}^{2} \) and it is 7 m broad. \( \begin{array}{ll}\text { (i) Find its length } & \text { (ii) Find its perimeter }\end{array} \)

Ask by Powell Mills. in Nepal
Feb 10,2025

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Tutor-Verified Answer

Answer

Length = 0.1 cm Perimeter = 1400.2 cm

Solution

We are given that the area of the rectangle is 70 cm² and that its breadth is 7 m. Notice that the units are different. Since the area is in square centimeters, we need to convert 7 m into centimeters. Step 1. Convert the breadth to centimeters.   7 m = 7 × 100 cm = 700 cm Step 2. Let the length be L (in cm). The area of a rectangle is given by:   Area = length × breadth So,   70 cm² = L × 700 cm Step 3. Solve for L:   L = 70 / 700 = 0.1 cm Step 4. Find the perimeter. The perimeter P of a rectangle is given by:   P = 2 × (length + breadth) Here, length = 0.1 cm and breadth = 700 cm, so:   P = 2 × (0.1 + 700) = 2 × 700.1 = 1400.2 cm Thus, the answers are:  (i) Length = 0.1 cm  (ii) Perimeter = 1400.2 cm Note: It is unusual for a rectangle with a breadth of 7 m (700 cm) to have an area of only 70 cm² because the calculated length comes out extremely small (only 0.1 cm). In many problems a misprint might occur (for example, the area might have been intended to be 70 m²); however, using the given values and performing the necessary unit conversion, these are the correct answers.

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Beyond the Answer

To find the length of the rectangle, we use the area formula: Area = Length × Breadth. Given that the area is \( 70 \, \text{cm}^2 \) and the breadth (width) is 7 m (which is 700 cm), we rearrange the formula to get Length = Area ÷ Breadth. So, Length = \( 70 \, \text{cm}^2 \div 700 \, \text{cm} = 0.1 \, \text{cm}\). Now for the perimeter: Perimeter = 2 × (Length + Breadth). With Length = \( 0.1 \, \text{cm} \) and Breadth = \( 700 \, \text{cm} \), the perimeter is \( 2 \times (0.1 + 700) = 2 \times 700.1 = 1400.2 \, \text{cm} \). So in summary, the length is \( 0.1 \, \text{cm} \) and the perimeter is \( 1400.2 \, \text{cm} \).

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