Question

The length of a rectangle 8 cm more than the breadth. If the perimeter of the rectangle is 80 cm,
then the area of the rectangle is
(a) 192 cm² (b) 364 cm² (c) 384 cm² (d) 382 cm²

Answer 1

Let l and b be the length and breadth of the rectangle, then l = b + 8.
Perimeter of rectangle = 2 (l + b)
= 2(l + l − 8)
= 4l − 16
$$\begin{gathered} \Rightarrow 80=4l-16 \\ \Rightarrow 4l=80+16=96 \\ \Rightarrow l=24\mathrm{cm} \\ \Rightarrow b=l-8=24-8=16\mathrm{cm} \end{gathered}$$
Area of rectangle = $l\times b=24\times 16=384{\mathrm{cm}}^2$
Hence, the correct option is (c).