Question

The breadth of a rectangle is w cm and the length is 5 times as long as its breadth. What is the perimeter of the rectangle?
 $$\begin{gathered} (a)\text{ 5}{\text{w}}^2 \\ (b)\text{ 12w} \\ (c)\text{ (10 + 2w)cm} \\ (d)\text{ (25 + }{\text{w}}^2)cm \end{gathered}$$

Answer 1

Hint: In this question use the direct formula for the perimeter of the rectangle which is given as p = 2(l + b). Use the relation between the length and the breadth given to find the final answer in terms of w only.

Complete step-by-step answer:

Given data
The breadth (b) of a rectangle = w cm, as shown in above figure.
And the length (l) of a rectangle is 5 times as long as its breadth.
 $\Rightarrow l=5w$ , as shown in above figure.
Now as we know that the perimeter (p) of any shape is the sum of all the sides.
So the perimeter of the rectangle is, p = 2(l + b)
Now substitute the values in the above equation we have,
 $\Rightarrow p=2\left(l+b\right)=2\left(5w+w\right)=12w$ cm.
So this is the required perimeter of the rectangle.
Hence option (B) is correct.

Note – There can be another method to find the answer to this problem. Perimeters can also be defined as the sum of all the sides. Thus if we use the property of a rectangle that the opposite sides of the rectangle are equal then all the lengths would have been known. Thus using this too right answer could be found.