Question

Area of a right-angled triangle is $6c{m}^2$ and its perimeter is $12cm$. Find its hypotenuse. (in cm)

• A. 5
• B. 6
• C. 7
• D. 8

Answer 1

Answer: (A)

Let the sides of the triangle (in $cm$ ) be $a,b$, and $c$, where $a<b<c$.
$\therefore c$ is the hypotenuse and $a$ and $b$ are the perpendicular sides.
Given, $a+b+c=12$(1)
$\frac{1}{2}(a)(b)=6$(2)
From Eq. (1) $\Rightarrow a+b=12-c$
Squaring both sides,
$a^2+b^2+2ab=12^2-24c+c^2$
$=a^2+b^2+4\left(\frac{1}{2}ab\right)=12^2-24c+c^2$
$\Rightarrow c^2+4(6)=12^2-24c+c^2$
$c=5$ .