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

Answer:

$Area = 336\ m^2$

Step-by-step 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:

$Area = \sqrt{p(p-a)(p-b)(p-c)}$

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

$p = P/2 = 42\ m$

So we have that:

$Area = \sqrt{42(42-26)(42-28)(42-30)}$

$Area = 336\ m^2$