Question

The height of a triangle is 5 units more than twice it's base. If the area of a triangles is 21 square units, what is its height?

Answer 1

See below

Explanation:

We know that Area of a triangle is given by `A=(bh)/2`

where `h=2b+5` and `A=21`. Then

`21=b(2b+5)/2`

`42=2b^2+5b` Then `2b^2+5b-42=0`

`b=(-5+-sqrt(25+4·42·2))/4=(-5+-19)/4`

There are two possible values for b `b=7/2` and `b=-6` rejected

With this value, substitution in `h=2b+5=2·7/2+5=12`

And both dimensions are now calculated.

`A=(7/2·12)/2=42/2=21`