Question

The length and breadth of a rectangle are (3x + 4) cm and (4x − 13) cm respectively. If the
perimeter of the rectangle is 94 cm, then its area is
(a) 432 cm² (b) 512 cm² (c) 542 cm² (d) 532 cm²

Answer 1

Here, l = (3x + 4) cm, b = (4x − 13) cm and Perimeter of rectangle = 94 cm.
Perimeter of rectangle = 2(l + b) = 2[(3x + 4) + (4x − 13)] = (14x − 18) cm
As per the question
14x − 18 = 94 $\Rightarrow x=\frac{94+18}{14}=8$
Now
l = 3 $\text{×}$ 8 + 4 = 28 cm
b = 4 $\text{×}$ 8 − 13 = 19 cm
Area of rectangle = l $\text{×}$ b = 28 $\text{×}$ 19 = 532 cm²
Hence, the correct option is (d).