The sides of a triangle are x, y and z, If x + y = 7 m, y + z = 9m, and z + x = 8 m, then area of the triangle is

To find the area of the triangle, we first need to find the lengths of the sides x, y, and z.

Given: x + y = 7m y + z = 9m z + x = 8m

We can solve these equations simultaneously to find the values of x, y, and z.

Adding all three equations, we get: 2x + 2y + 2z = 24m Dividing by 2, we get: x + y + z = 12m

Now, subtract the given equations from this result to find the values of x, y, and z:

x = 12m - 9m = 3m y = 12m - 8m = 4m z = 12m - 7m = 5m

So, the sides of the triangle are 3m, 4m, and 5m.

This is a Pythagorean triple, which means the triangle is a right triangle. The area of a right triangle is given by the formula 1/2 * base * height.

Here, we can take 4m as the base and 3m as the height (or vice versa, it doesn't matter in multiplication):

Area = 1/2 * 4m * 3m = 6 square meters.