34. The sides of a triangle are in the ratio 5:12:13, and its perimeter is 150 m. Find the area of the triangle
Question
34. The sides of a triangle are in the ratio 5:12:13, and its perimeter is 150 m. Find the area of the triangle.
Solution
Step 1: Find the lengths of the sides of the triangle
The sides of the triangle are in the ratio 5:12:13. This means that if we add up the parts of the ratio, we get 5 + 12 + 13 = 30 parts.
The perimeter of the triangle is given as 150 m. This means that each part of the ratio corresponds to 150 m / 30 = 5 m.
Therefore, the lengths of the sides of the triangle are 55 = 25 m, 125 = 60 m, and 13*5 = 65 m.
Step 2: Find the area of the triangle
The triangle is a Pythagorean triangle (since 5^2 + 12^2 = 13^2), so we can use the formula for the area of a right triangle, which is 1/2 * base * height.
Here, we can take 60 m as the base and 25 m as the height (or vice versa, it doesn't matter which one is the base and which one is the height in a right triangle).
So, the area of the triangle is 1/2 * 60 m * 25 m = 750 square meters.
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