Question

If the area of a triangle with base $x$ is equal to the area of a square with side $x$, then the length of altitude of the triangle is _________.

• A. $\frac{x}{2}$
• B. $x$
• C. $2x$
• D. $3x$

Answer 1

Answer: (C)

$2x$

Area of triangle $=\Delta =\frac{1}{2}\times \left(\text{base}\right)\left(\text{height}\right)$

Let altitude of the triangle is $=h$

and base $=x$

Given the area of a triangle with base $x$ is equal to the area of a square with side $x$

We know $\Delta =x^2$

$\Rightarrow \Delta =\frac{1}{2}\times x\left(\text{height}\right)=x^2$

$\Rightarrow h=2x$

Height / altitude of triangle is $2x$.