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. 65 cm
• D. 70 cm

Answer 1

The correct option is D 70 cm

ABCD is a rectangle where, the length $\left(l\right)AB=4x$ and breadth $\left(b\right)BC=3x$.
$AC$ and $BD$ are diagonals.


$△ABC$ is a right angled triangle.
$(diagonal{)}^2=l^2+b^2$
$\Rightarrow (25{)}^2=16x^2+9x^2$
$\Rightarrow 25x^2=625$
$\Rightarrow x^2=25\Rightarrow x=5$

$l=4x=4\times 5=20cm$
$b=3x=3\times 5=15cm$

Perimeter $=2(l+b)=2(20+15)=2\times 35=70cm$