Question

The area of the triangle below is 2 square centimeters. What is the length of thebase? Express your answer as a fraction in simplest form.

Answer 1

In a right triangle, the area is given by half of the product between the height and the base.

`A=(b* h)/(2)`

We already know the height and the area, if we plug those values on this formula we can solve it for the base

`(25)/(12)=(b*(5)/(3))/(2)`

Solving for b, we have

`\begin{gathered} (25)/(12)=(b*(5)/(3))/(2) \\ (25)/(12)*2=(b*(5)/(3))/(2)*2 \\ (25)/(6)=b*(5)/(3) \\ b=((25)/(6))/((5)/(3)) \\ b=(25)/(6)*(3)/(5) \\ b=(25*3)/(6*5) \\ b=(25)/(5)*(3)/(6) \\ b=5*(1)/(2) \\ b=(5)/(2) \end{gathered}`

The base is equal to 5/2 cm.