Question

The base of a right triangle is 2 meters greater than the height. If the area of the triangle is 100 m2, what are the dimensions of the base and the height?

Answer 1

b = 15.2 m

h = 13.2 m

Explanation:

The area of a right triangle is given by:

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

Where:

b: is the base

h: is the height

If the base is 2 meters greater than the height we have:

`b = h + 2` (2)

And if the area of the triangle is 100 m², the dimensions of the base can be found by entering equation (2) into (1):

`100 m^(2) = ((h + 2)*h)/(2)`

`200 m^(2) = h^(2) + 2h`

`h^(2) + 2h - 200 m^(2) = 0`

By solving the above quadratic equation we have:

`h = 13.2 m`

And by entering the above value into equation (2) we have:

`b = 13.2 + 2 m = 15.2 m`

Therefore, the dimensions of the base and the height are 15.2 m and 13.2 m respectively.

I hope it helps you!