Question:

The length and breadth of a rectangle are in the ratio 4 : 3. If the diagonal measures 25 cm then the perimeter of the rectangle is

(a) 56 cm

(b) 60 cm

(c) 70 cm

(d) 80 cm

Solution:

(c) 70 cm

Let $A B C D$ be a rectangle and let the diagonal $A C$ be $25 \mathrm{~cm}$, length $A B$ be $4 x \mathrm{~cm}$ and breadth $B C$ be $3 x$ cm.

Each angle of a rectangle is a right angle.

$\therefore \angle A B C=90^{\circ}$

From the right $\Delta A B C:$

$A C^{2}=A B^{2}+B C^{2}$

$\Rightarrow(25)^{2}=(4 x)^{2}+(3 x)^{2}$

$\Rightarrow 625=16 x^{2}+9 x^{2}$

$\Rightarrow 625=25 x^{2}$

$x^{2}=\frac{625}{25}=25$

$\Rightarrow x=5$

$\therefore L$ ength $=4 \times 5=20 \mathrm{~cm}$

Breadth $=3 \times 5=15 \mathrm{~cm}$

∴ Perimeter of the rectangle = 2(20+15) cm

= 70 cm