Question

The area of the triangle below is40 square meters. What is the length of the base?Express your answer as a fraction in simplest form.

Answer 1

Given the area of the triangle:

$A=\frac{3}{40}m^2$

You can identify in the figure provided in the exercise that the height of the triangle is:

$h=\frac{1}{5}m$

The area of a triangle can be calculated using this formula:

$A=\frac{bh}{2}$

Where "A" is the area, "b" is the base, and "h" is the height.

If you solve for "b", you obtain this formula:

$\begin{gathered} 2A=bh \\ \\ b=\frac{2A}{h} \end{gathered}$

Therefore, knowing the Area and the height of the triangle, you can substitute them into the formula and then evaluate, in order to find the length of its base:

$b=\frac{(2)(\frac{3}{40})}{\frac{1}{5}}$$b=\frac{\frac{6}{40}^{}}{\frac{1}{5}}$$b=\frac{6\cdot5}{40\cdot1}$$b=\frac{30}{40}$$b=\frac{3}{4}m$

Hence, the answer is:

$b=\frac{3}{4}m$