Question

If the difference between the sides of a right angled triangle is $3$ cm and its area is $54c{m}^2$, find its perimeter.

• A. $30$ cm
• B. $36$ cm
• C. $49$ cm
• D. $81$ cm

Answer 1

The correct option is B $36$ cm

Let one side $=a$, other side $=b$
Given, difference between sides, $a-b=3$
Area of triangle $=\frac{a(a-3)}{2}=54$
$a^2-3a=108$
$a=12,a=-9$
$c=\sqrt{{12}^2+9^2}=\sqrt{144+81}=\sqrt{225}=15$
$\therefore c=15$
$\therefore$ perimeter of triangle $=15+12+9=36$ cm