Question

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

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

Answer 1

The correct option is D $2x$

Given area of triangle is equal to area of square.

Let altitude of traingle be $a$ .

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

$=\frac{1}{2}x\times a$

Area of square $={\text{(side)}}^2=x^2$

Given both are same

$\Rightarrow \frac{x\times a}{2}=x^2$

$\Rightarrow a=\frac{2x^2}{x}=2x$

Therefore, altitude $=2x$

Option (D) is correct.