SOLUTION: If the ratio of the side lengths of a triangle is 2:3:4 and the shortest side is 15 in. What is the perimeter?

Algebra ->  Triangles -> SOLUTION: If the ratio of the side lengths of a triangle is 2:3:4 and the shortest side is 15 in. What is the perimeter?      Log On


   

Question 825638: If the ratio of the side lengths of a triangle is 2:3:4 and the shortest side is 15 in. What is the perimeter?
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--

THE PROBLEM:
If the ratio of the side lengths of a triangle is 2:3:4 and the shortest side is 15 in. What is the 
perimeter?

A SOLUTION:
First we find each side lengths using the ratios of one side to another. Then we add together 
the side length to get the perimeter.

Step 1: Define variables.
Let x be the shortest side.
Let y be the longest side.
Let z b the third side.

The shortest side is 15 inches, so x = 15.

The ratio of shortest side to longest side is 2 to 4. Our ratio is 
x%2Fy=2%2F4
15%2Fy=2%2F4

Solve for y.
2y+=+%2815%29%284%29
2y+=+60
y+=+30

The longest side is 30 inches.

The ratio of the third side to the longest side is 3 to 4. Our ratio is
z%2Fy=3%2F4
z%2F30=3%2F4

Solve for z.
4z=%2830%29%283%29
4z=90
z+=+22.5

The third side measures 22.5 inches.

The perimeter is the sum of the side lengths, or x+y+z

x%2By%2Bz=15%2B30%2B22.5=67.5

The perimeter is 67.5 inches.


Hope this helps!

Mrs. Figgy
math.in.the.vortex@gmail.com