Question

If the sides of a triangle are 4 cm, 6 cm and 6 cm, then find the height corresponding to the smallest side.

• A. 8$\sqrt{2}$
• B. 4$\sqrt{2}$
• C. 16$\sqrt{2}$
• D. 7$\sqrt{2}$

Answer 1

The correct option is B

4$\sqrt{2}$

$S=\frac{Perimeter}{2}=\frac{(a+b+c)}{2}=\frac{(4+6+6)}{2}=8cm$

Area of the triangle =$\sqrt{s(s-a)(s-b)(s-c)}$ = $\sqrt{8(8-4)(8-6)(8-6)}$ = $\sqrt{128}=8\sqrt{2}{cm}^2$

Area of a triangle is also find using $\frac{1}{2}\times base\times height$

$\Rightarrow 8\sqrt{2}=\frac{1}{2}\times 4\times height$

$\Rightarrow height=4\sqrt{2}cm$.