Question

The ratio of the side lengths of a triangle is 2:3:4. The shortest side is 15 inches. What is the perimeter? Explain.

Answer 1

Answer:

The perimeter is equal to $67.5\ in$

Step-by-step explanation:

In this problem we have a ratio of three numbers

$2:3:4$

Let

x------> the first side (shortest side)

y------> the second side

z------> the third side

we know that

$\frac{x}{y}=\frac{2}{3}$ --> $y=\frac{3}{2}x=1.5x$ ----> equation A

$\frac{x}{z}=\frac{2}{4}$ ---> $z=\frac{4}{2}x=2x$ -----> equation B

$x=15\ in$

Substitute the value of x in the equation A and equation B

$y=1.5(15)=22.5\ in$

$z=2(15)=30\ in$

Find the perimeter of triangle

Remember that the perimeter is equal to the sum of the length sides

$P=x+y+z=15+22.5+30=67.5\ in$

Answer 2

First, look at the ratio. And out of 2&3&4, 2 is the smallest. So, change the 2 to 15, 3 to X, 4 to Y. Like this down below

15:X:Y 

Now, if 2=15, 1=15÷2, which is 7.5

If one is 7.5, the X=3×7.5=22.5

Y=4×7.5=23

Add them all up, 15+22.5+23=60.5

The perimeter is 60.5