Question

The perimeter of a rectangle is $64$ cm. If the ratio of the lengths of two adjacent sides is $7:9$, find the lengths of these sides.

• A. $14cmand18cm$
• B. $15cmand20cm$
• C. $12cmand15cm$
• D. $14cmand16cm$

Answer 1

Answer: (A)

$14cmand18cm$

Let the length of two adjacent sides be $x$ and $y$ respectively.

The ratio of the length of two adjacent sides is $x:y=7:9$

$\Rightarrow \frac{x}{y}=\frac{7}{9}$

$\Rightarrow x=\frac{7y}{9}$ .......$\left(1\right)$

Given:Perimeter of the rectangle$=2\times$(sum of the length of two adjacent sides)

$\Rightarrow 64=2(x+y)$

$\Rightarrow 64=2(\frac{7y}{9}+y)$

$\Rightarrow 64=2\left(\frac{7y+9y}{9}\right)$

$\Rightarrow 16y=32\times 9$

$\Rightarrow y=\frac{32\times 9}{16}=2\times 9=18$ cm

Substitute the value of $y=18$cm in $\left(1\right)$ we get

$x=\frac{7y}{9}=\frac{7\times 18}{9}=7\times 2=14$ cm

Hence the length of two adjacent sides are $14$ cm and $18$ cm