Consider that the ratio of the side lengths of a triangle is 2:3:4. We want to find the perimeter of the triangle if the shortest side is 15 inches. To do so, let's start by define the side lengths.
x as the shortest side.
y as the longest side.
z as the middle side.
This means that the ratio x:y is equal to ratio of the shortest and longest side, 2:4. The same will occur with the value of the ratios.
x/y=2/4In our case, the shortest side is x= 15. Let's substitute this value into the equation and solve for y.
This means that the longest side in the triangle is 30 inches long. Now we can use a similar procedure for the third side. This time the ratio z:y will be equal to the ratio of the middle side and the longest side.
z/y=3/4
The longest side of the triangle is y= 30. Let's substitute this value into the equation and solve for z.
The middle side is 22.5 inches long. Finally, let's calculate the perimeter by adding the three side lengths.
P=15+30+22.5 → P=67.5
The perimeter of the triangle is 67.5 inches.
