Question

The area of a rectangle is $300c{m}^2$ and its length: breadth $=4:3$. Find
(i) its perimeter
(ii) the length of its diagonal.

Answer 1

$\frac{length}{breadth}=\frac{4}{3}$

Breadth$=\frac{3}{4}\times$

$b=\frac{3}{4}l$

Area$=l\times b=300$

$l\times \frac{3}{4}l=300$

$\frac{3}{4}{l}^2=300$

$l^2=100\times 4$

$l^2=400$

$l=20cm$

$b=\frac{3}{4}l$

$=\frac{3}{4}\left(20\right)=3\left(5\right)=15$

Perimeter$=2(l+b)$

$=2(20+15)$

$=2\left(35\right)=70cm$

In $△ABD$

${AB}^2+{AD}^2={BD}^2$

$400+225={BD}^2$

${BD}^2=625$

$BD=25cm$

$\therefore$Length of diagonal$=25cm$