Question

If the ratio of sides of a rectangle is 2 : 7 and perimeter is 360 m, then find out its length and breadth.

• A. 140m, 40m
• B. 144m, 36m
• C. 160m, 20m
• D. 135m, 45m

Answer 1

The Correct Option is A

Given the ratio of sides of a rectangle is 2:7 and the perimeter is 360 meters, we can find the length and breadth as follows:
Let the sides of the rectangle be \( 2x \) and \( 7x \).
The perimeter of a rectangle is given by:
\[ 2 \times (\text{length} + \text{breadth}) = 360 \]
Substituting the given ratio:
\[ 2 \times (2x + 7x) = 360 \]
\[ 2 \times 9x = 360 \]
\[ 18x = 360 \]
\[ x = 20 \]
Therefore, the length and breadth are:
\[ \text{Length} = 7x = 7 \times 20 = 140 \text{ m} \]
\[ \text{Breadth} = 2x = 2 \times 20 = 40 \text{ m} \]
Answer: A (140m, 40m)

Answer 2

Since the sides are in the ratio 2:7, together they make up 9 equal parts, and these 9 parts add up to the semi-perimeter (half the perimeter).

Semi-perimeter \(=\frac{360}{2}=180\) m.

Length (7 parts out of 9):
\[\frac{7}{9}\times180=140\text{ m}\]
Breadth (2 parts out of 9):
\[\frac{2}{9}\times180=40\text{ m}\]

1. Option A (140m, 40m): Matches exactly.
2. Option B (144m, 36m): Does not match the 2:7 proportion of 180.
3. Option C (160m, 20m): Does not match.
4. Option D (135m, 45m): Does not match.

The length and breadth of the rectangle are 140 m and 40 m.

Hence, the correct answer is Option A: 140m, 40m.