# The perimeter of a triangle is 24 inches. The longest side of 4 inches is longer than the shortest side, and the shortest side is three-fourths the length of the middle side. How do you find the length of each side of the triangle?

Feb 24, 2016

Well this problem is simply impossible.

If the longest side is 4 inches, there is no way that the perimeter of a triangle can be 24 inches.

You are saying that 4 + (something less than 4) + (something less than 4) = 24, which is impossible.

Feb 24, 2016

The sides are $6$ inches, $8$ inches and $10$ inches

#### Explanation:

I'd suggest that the question should read 'The perimeter of a triangle is 24 inches. The longest side is 4 inches longer than the shortest side, and the shortest side is three-fourths the length of the middle side. How do you find the length of each side of the triangle?'

In this case the question can be answered. If $x$ is the length of the middle side, then the shortest side is $\frac{3}{4} x$ and the longest side is $\frac{3}{4} x + 4$

$x + \frac{3}{4} x + \frac{3}{4} x + 4 = 24$

$\frac{10}{4} x = 20$
$x = 8$

Then the shortest side is $6$ and the longest side is $10$