Question

Two rectangles have the same perimeter. Length and breadth are in the ratio 2 : 3 in The 1st and 3 : 4 in the 2nd.

The 1st one 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 it as x

Length and breadth of 1st rectangle are $\frac{3}{5}$x and $\frac{2}{5}$x

Area = $\frac{3}{5}\times \frac{2}{5}$ = $\frac{6}{25}{x}^2$

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 $\frac{6}{25}$ and $\frac{12}{49}$

We get , $\frac{12}{49}$ > $\frac{6}{25}$

Hence, Area of 2nd rectangle is Larger and the Given statement is False.