Question

The length of a rectangle is twice its breadth. If the perimeter is 30 cm, find out the area of the rectangle in square centimetres.

• A. 50
• B. 84
• C. 40
• D. 65

Answer 1

The correct option is A 50

Let the breadth of the rectangle be x cm.
Length of the rectangle = 2x cm

Given: Perimeter = 30 cm
Therefore, 2(length + breadth) = 30
2(2x + x) = 30
2(3x) = 30
6x = 30
If x = 3, 6x $=6\times 3=18\ne 30$
If x= 4, 6x $=6\times 4=24\ne 30$
If x = 5, 6x $=6\times 5=30$
Therefore, if x = 5, LHS = RHS.

So, breadth = 5 cm
Therefore, length = 2$\times$breadth = 2$\times$5 = 10 cm
Hence, area of the rectangle = (length $\times$breadth) = 10$\times$5 = 50 $c{m}^2$