Question

The area of the triangle below is7 square centimeters. What is the length of thebase? Express your answer as a fraction in simplest form.

Answer 1

The first thing we have to know is that the area of the triangle is given by the following equation

`A=(b\cdot h)/(2)`

Where

• A = area

• b = base

• h = height

From our exercise we have the area and the height, so we clear the base to be able to calculate it

`\begin{gathered} A=(b\cdot h)/(2) \\ 2A=b\cdot h \\ b=(2A)/(h) \end{gathered}`

Using the base equation we substitute our values

`\begin{gathered} A=(2)/(15)cm^2 \\ h=(2)/(5)cm \end{gathered}`
`\begin{gathered} b=(2(2/15))/(2/5) \\ b=(4/15)/(2/5) \\ b=(4\cdot5)/(2\cdot15) \\ b=(20)/(30) \\ b=(2)/(3)cm \end{gathered}`

The base of the triangle measures 2/3 cm