Tick (✓) the correct answer:
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
(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
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