Question

The base of a triangle is 3 inches shorter than twice the height. If the area is 10 inches squared,

what is the base and the height?

Answer 1

height = 4 in

base = 5 in

Explanation:

The area of a triangle can be found using the equation:

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

where
`b` is the base of the triangle and
`h` is the base.

In order to plug into this equation, we need to use the relationship between the base and height. It is given that the base is 3 inches shorter than twice the height. Converting this to a mathematical equation:

`b = 2h-3`

Since we are given that the area is 10 inches squared, we can now plug into the area equation to solve for the height (using the quadratic formula):

`10 = (1)/(2) (2h-3)(h)\\2h^2 - 3h -20 = 0\\h = 4`

** We reject the negative solution of -5/2, since the triangle's height cannot be negative.

Now, we can simply plug in this height to solve for the base:

`b = 2(4) - 3\\b = 5`