Question

If the area of a triangle is $54c{m}^2$ and its height is three times its base, then find the base.

• A. $6cm$
• B. $7cm$
• C. $6.5cm$
• D. $7.5cm$

Answer 1

The correct option is A $6cm$

Area of a triangle $=\frac{1}{2}\times \text{base}\times \text{height}$

Let the base be $x$.

$\Rightarrow$ height $=3x$

$\Rightarrow 54=\left(\frac{1}{2}\right)\times x\times 3x$

$\Rightarrow 3x^2=108$

$\Rightarrow x^2=36$

$\Rightarrow x=\pm 6$

Now, we know that base cannot be negative.

$\therefore$ base $=6cm$