Question

The length of and breadth of a rectangle are (3x + 4) cm and (4x − 13) cm. If the perimeter of the rectangle is 94 cm, then x =

(a) 4 (b) 8 (c) 12 (d) 6

Answer 1

Here, l = (3x + 4) cm and b = (4x − 13) cm.
Perimeter of rectangle = 2 (l + b)
= 2[(3x + 4) + (4x − 13)]
= 2(7x − 9) = 14x − 18
Now, as per the question
Perimeter of rectangle = 94 cm
$$\begin{gathered} \therefore 14x-18=94 \\ \Rightarrow 14x=94+18=112 \\ \Rightarrow x=\frac{112}{14}=8 \end{gathered}$$
Hence, the correct option is (b).