Question

Two rectangles have the same perimeter. length and breadth are in the ratio 5 : 2 in the 1st and 4 : 3 in the 2nd rectangle.

The 1st rectangle has greater area.

• A. True
• B. False

Answer 1

The correct option is B

False

Given that perimeters are same. So, sum of lengths and breadths are also the same. Let's take perimeter for each rectangle as $x$

Length and breadth of 1st rectangle are $\frac{5}{7}x$ and $\frac{2}{7}x$

Area = $\frac{5}{7}\times \frac{2}{7}=\frac{10}{49}{x}^2$

Length and breadth of 2nd rectangle are $\frac{4}{7}x$ and $\frac{3}{7}x$

Area = $\frac{4}{7}\times \frac{3}{7}=\frac{12}{49}{x}^2$

Comparing $\frac{10}{49}$ and $\frac{12}{49}$

We get , $\frac{12}{49}>\frac{10}{49}$

Hence, area of 2nd rectangle is larger and the given statement is False.