Question

If the area of a triangle is $49c{m}^2$ and its base is double the corresponding height, then find the height of the triangle.

• A. 6 cm
• B. 9 cm
• C. 24 cm
• D. 7 cm

Answer 1

The correct option is D

7 cm

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

Let the height be $x$.

$\Rightarrow$ base $=2x$

$\Rightarrow$ $49=\left(\frac{1}{2}\right)\times 2x\times x$
(Since area of the triangle is 49 cm${}^2$)

$\Rightarrow x^2=49$

$\Rightarrow x=\pm 7$

Now, we know that height of the triangle cannot be negative.

$\therefore$ height $=7cm$