Difficulty: Easy
Correct Answer: 62
Explanation:
Introduction / Context:
This problem involves finding the perimeter of a rectangle when its length and breadth are known. Perimeter is the distance around the boundary of the rectangle. The question reinforces the basic formula for the perimeter of a rectangle, which is commonly used in everyday contexts such as fencing a garden or framing a picture.
Given Data / Assumptions:
Concept / Approach:
The perimeter of a rectangle is twice the sum of its length and breadth because each dimension appears on two opposite sides. Therefore P = 2(L + B). We add 24 and 7, then multiply by 2 to obtain the perimeter in centimetres. The process is simple and is a direct application of the formula.
Step-by-Step Solution:
Length L = 24 cm, breadth B = 7 cm.Perimeter P = 2(L + B).Compute L + B = 24 + 7 = 31.Now P = 2 * 31 = 62 cm.Hence the perimeter of the rectangle is 62 centimetres.
Verification / Alternative check:
Another way is to add all four sides separately. The rectangle has two lengths of 24 cm and two breadths of 7 cm. Adding gives 24 + 7 + 24 + 7 = (24 + 24) + (7 + 7) = 48 + 14 = 62 cm. This matches the result from the formula and confirms our answer is correct.
Why Other Options Are Wrong:
124 is obtained if someone multiplies 62 by 2 again, misinterpreting the formula. 48 is only the sum of the two lengths, ignoring the breadths. 96 could result from incorrectly using 4 * 24 or 4 * some average value, and 68 is a near miss from simple addition mistakes. None of these match the correct formula and calculation for perimeter.
Common Pitfalls:
Many learners confuse area and perimeter formulas. Area of a rectangle is L * B, while perimeter is 2(L + B). Another common mistake is to add 2L + B instead of 2(L + B). Visualising the rectangle and tracing its boundary can help remember that each side length is counted twice. Always double check that you have included both length and breadth twice in the perimeter calculation.
Final Answer:
62
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