Question

The base of triangle is 2x + 2 and the height of the triangle is x. Find the measure of the base and the height of the height of the area is 20 ft^2

Answer 1

Length of the base = 10

Length of the height = 4

Explanation:

Remember that the area of a triangle is given by the formula

`A=(1)/(2) bh`

where

`A` is the area

`b` is the base

`h` is the height

We know from our problem that the base of the triangle is 2x + 2, so
`b=2x+2`. We also know that its height is x and its area is 20 ft^2, so
`h=x` and
`A=20`. Let's replace the values in our formula to find
`x`:

`A=(1)/(2) bh`

`20=((1)/(2) )(2x+2)(x)`

`20=((1)/(2) )2(x+1)(x)`

`20=x(x+1)`

`20=x^2+x`

`x^2+x-20=0`

`(x-4)(x+5)=0`

`x=4` or
`x=-5`

Since distance cannot be negative,
`x=4`

Now we can substitute the value for
`x` in the base and height:

base =
`2x+2`

base =
`2(4)+2`

base =
`8+2`

base =
`10`

height =
`x`

height =
`4`