Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
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
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
