Final answer:
To find the altitude of the triangle, we can use the formula for the area of a triangle and set up a quadratic equation. Solving the equation will give us the altitude of the triangle.
Step-by-step explanation:
To solve this problem, we can use the formula for the area of a triangle: Area = (base * altitude) / 2. Let's assume the altitude of the triangle is h and the base is 2h + 18. We are given that the area is 360 sq. m., so we can set up the following equation:
360 = (2h + 18) * h / 2
Simplifying this equation, we get:
720 = (2h + 18) * h
Expanding and rearranging, we have:
2h² + 18h - 720 = 0
We can now solve this quadratic equation using factoring, completing the square, or the quadratic formula. Once we find the value of h, we will have the altitude of the triangle.
The problem can be solved using the formula for the area of a triangle and substituting the given conditions into this equation. This will form a quadratic equation that can be used to determine the altitude of the triangle.
The subject of the question is mathematics and it addresses geometric problem solving related to triangles. To solve the problem, you need to understand that the area (A) of a triangle is given by the formula A = 1/2 base (b) times altitude (h), or A = 1/2bh. According to the problem, the base of the triangle is more than twice the altitude by 18m, which can be represented as b = 2h+18. The area of the triangle is 360 square meters.
First, we substitute the given area and the base in terms of altitude into the area formula: 360m = 1/2 * (2h+18) * h. Simplifying gives, 360m = (h+9) *h. Solving this equation will provide the altitude of the triangle.
Learn more about Triangle Geometry