Question

The height of a triangle is 5 m less than half its base. If the area of the triangle is 300 m2, how do you find the measure of the height?

Answer 1

height`=15" meters"`

Explanation:

The formula for area of the triangle is `A = (bh)/2`.

Let the base be `b` and the height be `b/2 - 5`.

Then:

`300 = (b(b/2 - 5))/2`

`600 = b(b/2 - 5)`

`600 = b^2/2 - 5b`

`600 = (b^2 - 10b)/2`

`1200 = b^2 - 10b`

`b^2 - 10b - 1200= 0`

Solve by completing the square:

`1(b^2 - 10b + 25 -25) = 1200`

`1(b^2 - 10b + 25) - 25 = 1200`

`(b - 5)^2 = 1225`

`b - 5 = +-35`

`b = -30 and 40`

Hence, the base measures #40" meters" (a negative length is impossible).

The height therefore measures `40/2 - 5 = color(green)(15)`

Hopefully this helps!