Question

The perimeter of a triangular field is 84 m, if the ratio of its sides are 13: 14:15, Find the area of the field. *

Answer 1

`Area = 336\ m^2`

Explanation:

If the ratio of the sides is 13:14:15, we can say that the length of each side is 13x, 14x and 15x.

Then, if the perimeter is 84 m, we have:

`P = 13x + 14x + 15x = 84`

`42x = 84`

`x = 2`

The length of each side is:

`13x = 26\ m`

`14x = 28\ m`

`15x = 30\ m`

Now, to find the area of the field, we can use the following formula:

`Area = √(p(p-a)(p-b)(p-c))`

Where a, b and c are the sides and p is the semi perimeter:

`p = P/2 = 42\ m`

So we have that:

`Area = √(42(42-26)(42-28)(42-30))`

`Area = 336\ m^2`