Question

An area of triangle is $x^2-x-2$ and and a base of $x+1$. Calculate the height of the triangle.

• A. $\frac{1}{2}(x+2)$
• B. $x-2$
• C. $2(x-2)$
• D. $(x-2){(x+1)}^2$

Answer 1

The correct option is C $2(x-2)$

Area of the triangle $=$ $x^2-x-2$

Base of the triangle $=$ $x+1$

Let the height of the triangle is $h$

Area of the triangle $=$ $\frac{1}{2}\times$Base$\times$height

$\therefore x^2-x-2=\frac{1}{2}\times (x+1)\times h$

$\frac{1}{2}\times x+1\times h=x^2-2x+x-2$

$\frac{1}{2}\times (x+1)\times h=x(x-2)+1(x-2)$

$\frac{1}{2}\times (x+1)\times h=(x-2)(x+1)$

$h=\frac{2(x-2)(x+1)}{x+1}$

$\Rightarrow h=2(x-2)$