Question 1006063

The sides of a triangle are in the ratio 5:12:13 and its perimeter is 150 m. Find the area of triangle.
<pre>A triangle with sides 5, 12, and 13 represents a special right triangle. That's because {{{5^2 + 12^2 = 13^2}}}
To determine the length of each side, we let the multiplicative factor for the sides, be x
Therefore, the sides are: 5x, 12x, and 13x
With the perimeter being 150, we get: 5x + 12x + 13x = 150
30x = 150 
x = {{{150/30}}}, or 5

We now have the sides as:
5(5), or  25 m
12(5), or 60 m
13(5), or 65 m

Obviously, the 2 shorter sides are the legs, with either leg being the altitude
Area: {{{(1/2)bh}}} = {{{(1/2)(25)(60)}}}, or {{{highlight_green(750 m^2)}}}