Question

Find the Length of all sides of the given right angled triangle if the area is 36 $c{m}^2$

• A. AB = 6cm , BC = 12cm, CA = 18
• B. AB = 12cm , BC = 6cm, CA = 6$\sqrt{3}$
• C. AB = 12cm , BC = 6cm, CA = 3$\sqrt{6}$
• D. AB = 6cm , BC = 12cm, CA = 6$\sqrt{3}$

Answer 1

The correct option is B

AB = 12cm , BC = 6cm, CA = 6$\sqrt{3}$

Area = $\frac{1}{2}$ $\times$(2x)$\times$(x) = 36
Solving for x we get:

$x^2$ = 36

$\Rightarrow$x = 6 cm, 2x = 12 cm

By Pythagora's theorem we get:

$2x^2$ + $x^2$ = $H^2$

$\Rightarrow$ $H^2$ = 3 $\times$ 36 = 108

$\Rightarrow$ H = 6$\sqrt{3}$