Question

15) 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?
Usen traductor ​

Answer 1

We determine the dimensions of a right triangle.

The area 100 m^2 is a function of the base (B) and the height (H):

$A = \frac{B\cdot H}{2} = 100$

The base is 2 meters greater than the height:

$B=H+2$

Then the area is a function of the height:

$\frac{(H+2)H}{2} =100\\\\H^2+2H-200=0$

Solving the second grade equation:

$H_1=13.18\\\\H_2=-15.18$

Negative solution is discarded, the dimensions are:

$H=13.18\\\\B=H+2=15.18$