Question

The height of a triangle is 3 m more than its base. If the area of the triangle is 35 sq.m. , then find its height.

• A. $10m$
• B. $7m$
• C. $14m$
• D. $5m$

Answer 1

The correct option is A $10m$

Let $x$ be the height of the triangle, then $(x-3)$ will be the base.

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

$\Rightarrow \frac{1}{2}\times (x-3)\times x=35$
$\Rightarrow (x-3)\times x=35\times 2$
$\Rightarrow x^2-3x=70$
$\Rightarrow x^2-3x-70=0$
$\Rightarrow (x-10)(x+7)=0$
$\Rightarrow x=10or(-7)$

$x$ cannot be a negative value. So $x=10.$

$\therefore$ The height of the triangle is 10 m.