Question

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

• A. 8√2
• B. 4√2
• C. 16√2
• D. 7√2

Answer 1

The correct option is B

4√2

Semi-perimeter of the triangle,

$s=\frac{\text{Perimeter}}{2}=\frac{(a+b+c)}{2}$

$=\frac{(4+6+6)}{2}=8cm$

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 can also be found using $\frac{1}{2}\times \text{base}\times \text{height}$

$\Rightarrow 8\sqrt{2}=\frac{1}{2}\times 4\times \text{height}$ [smallest side is $4cm$]

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