In a rectangle, the length and breadth are in the ratio $5 : 3$ . What is the ratio between its perimeter and area when the length is $15 m$ ?

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Solution

Step 1: Finding the breadth
Let length $= 5 x$
and breadth $= 3 x$
Given, length $= 15 m$
So,
$5 x = 15 m \Rightarrow x = \frac{15}{5} m \Rightarrow x = 3 m$
Then breadth $= 3 x = 3 \times 3 m = 9 m$
Step 2: Finding the perimeter of the rectangle
$\begin{array}{rcl} P e r i m e t e r o f r e c \tan g l e & = & 2 (l e n g t h + b r e a d t h) \\ = & 2 (15 + 9) \\ = & 2 \times 24 \\ = & 48 m \end{array}$
Thus, the perimeter of the rectangle is $48 m$
Step 3: Finding the area of the rectangle
$\begin{array}{rcl} A r e a o f r e c \tan g l e & = & l e n g t h \times b r e a d t h \\ = & 15 \times 9 = 135 m^{2} \end{array}$
Thus, the area of the rectangle is $135 m^{2}$
Step 4: Finding the ratio of perimeter and area
Since the perimeter of the rectangle is $48 m$ and the area of the rectangle is $135 m^{2}$
Thus,
$\begin{array}{rcl} r a t i o & = & \frac{p e r i m e t e r}{a r e a} \\ = & \frac{48}{135} \\ = & \frac{16}{45} \end{array}$
Hence, the ratio of perimeter and area is $16 : 45$

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