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

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.