Question

The length of the sides of a triangle are in the ratio 5:12:13,if the perimeter of the triangle is 105.Find the area of the triangle ?

Answer 1

The area is `367.5` units squared

Explanation:

The ratio of the sides is 5:12:13. That does not mean the lengths are 5, 12, and 13. That simply means that putting the side lengths into a ratio of shortest side:second shortest side:longest side, the ratio will be simplified to 5:12:13. Equivalent ratios are like equivalent fractions; they can be derived by multiplying each number in the ratio (5, 12, 13) by the same number.

Let's set up an equation with `x` as the unknown number of times 5, 12, and 13 (the ratio) are being multiplied:

`5x+12x+13x=105`

`30x=105`

`x=3.5`

That means the side lengths are `17.5, 42, 45.5` units, respectively (in the ratio 5:12:13)

It just so happens that this is a right triangle (`5^2+12^2=13^2`)

That means the two shorter sides need to be multiplied (height times base) and divided by 2.

`(17.5xx42)/2=735/2=367.5`