Respuesta :
Answer: height = 10 meters
base = 25 meters
Explanation:
Let h represent the height of the triangle. From the information given, the base of the triangle is five more than twice the height. This means that
base = 2h + 5
Recall, the formula for calculating the area of a triangle is
Area = 1/2 x base x height
Given that area of triangle = 125 square meters, then
125 = 1/2 x (2h + 5) x h
By cross multiplying,
2 x 125 = h(2h + 5)
h(2h + 5) = 250
2h^2 + 5h = 250
2h^2 + 5h - 250 = 0
This is a quadratic equation. We would solve by applying the method of factorization. The first step is to multiply 2h^2 with - 250. It becomes - 500h^2. We would find two terms such that their sum or difference is 5h and their product is - 500h^2. The terms are 25h and - 20h. By replacing 5h with 25h - 20h, we have
2h^2 + 25h - 20h - 250 = 0
We would factorize by grouping. We have
h(2h + 25)- 10(2h + 25) = 0
base =
Since h + 25 is common, it becomes
(h - 10)(h + 25) = 0
h - 10 = 0 or h + 25 = 0
h = 10 or h = - 25
The height cannot be negative. Thus,
height = 10 meters
base = 2 x 10 + 5 = 20 + 5
base = 25 meters
