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=(3)/(40)m^2`

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

`h=(1)/(5)m`

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

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

Hence, the answer is:

`b=(3)/(4)m`