Question

The height of a triangle is 7 m more than its base. If the area of the triangle is 39 sq.m. , then find its height.

• A. $10m$
• B. $13m$
• C. $14m$
• D. $6m$

Answer 1

The correct option is B $13m$

Let $x$ be the height of the triangle, then $(x-7)$ will be the base.

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

$\Rightarrow \frac{1}{2}\times (x-7)\times x=39$
$\Rightarrow (x-7)\times x=39\times 2$
$\Rightarrow x^2-7x=78$
$\Rightarrow x^2-7x-78=0$

For a quadratic equation $a{x}^2+bx+c$,
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here $a=1,b=-7$ and $c=-78$

So, $x=\frac{-(-7)\pm \sqrt{(-7{)}^2-4\times 1\times -78}}{2}$

$x=\frac{7\pm \sqrt{361}}{2}=\frac{7\pm 19}{2}$

$x=13orx=-6$

$x$ cannot be a negative value. So $x=13$

$\therefore$ The height of the triangle is 13 m.