Question

The measures of two adjacent sides of a rectangle are in ratio $7:5$. If the perimeter of the rectangle is $336cm$, find its area.

Answer 1

Step 1 : Finding the dimension of rectangle

Given that, sides of rectangle are in ratio $7:5$

Let sides of the rectangle be $7k,5k$

Now,

Perimeter of rectangle$=$ $2(length+breadth)$

$$\begin{gathered} 336=2(7k+5k) \\ 336=2(12k) \\ 336=24k \\ k=\frac{336}{24} \\ k=14 \end{gathered}$$

Thus ,sides of rectangle are

$$\begin{gathered} 7k=7\times 14=98cm \\ 5k=5\times 14=70cm \end{gathered}$$

Step 2: Calculating area of rectangle:

Area of rectangle $=length\times breadth$

$$\begin{gathered} =98\times 70 \\ =6860c{m}^2 \end{gathered}$$

Hence, area of rectangle is $6860c{m}^2$