Answer:
b = 15.2 m
h = 13.2 m
Step-by-step explanation:
The area of a right triangle is given by:
[tex] A = \frac{bh}{2} [/tex] (1)
Where:
b: is the base
h: is the height
If the base is 2 meters greater than the height we have:
[tex]b = h + 2[/tex] (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):
[tex]100 m^{2} = \frac{(h + 2)*h}{2}[/tex]
[tex] 200 m^{2} = h^{2} + 2h [/tex]
[tex] h^{2} + 2h - 200 m^{2} = 0 [/tex]
By solving the above quadratic equation we have:
[tex] h = 13.2 m [/tex]
And by entering the above value into equation (2) we have:
[tex]b = 13.2 + 2 m = 15.2 m[/tex]
Therefore, the dimensions of the base and the height are 15.2 m and 13.2 m respectively.
I hope it helps you!
