Question

The height of a triangle is four times the length of the base. What is the base and height of the triangle if the area is 18 square inches?

Answer 1

`color(white)(xx)a=3` and `h=12`

Explanation:

Let height be h, base be a, and area be A:

`color(white)(xx)h=4a`

`color(white)(xx)(ah)/2=A` `color(white)(xxxxxxxxxxxxx)`(area formula)
`=>color(red)(4a^2)/2=color(red)18`
`=>color(red)(1/2xx)(4a^2)/2=color(red)(1/2xx)18`

Take the squareroot of both sides:
`=>sqrt(a^2)=sqrt9`
`=>a=3`

`color(white)(xx)h=4xx3`
`color(white)(xxx)=12`