Jim J. answered • 09/21/22
Certified, highly experienced tutor of Algebra 1.
Hi Lesly,
In order to answer this question, you have to be able to write an equation. The equation will be for Perimeter which is the sum of the sides. If we let S be the length of the short side, M be the length of the medium side, and L be the length of the large side, then S + M + L = 27 (which is the perimeter).
This equation is not very helpful for finding the length of the sides because there are 3 different variables. Since we only have 1 equation, we need to write this equation with only 1 variable. So, let’s turn the words in the problem into mathematical expressions.
The first sentence says “The shortest side of the triangle is 8 inches less than the medium side.” If M is the medium side, then S must be M - 8.
S = M - 8
If I replace S with M - 8 in our perimeter equation, we will have:
S + M + L = 27
(M - 8) + M + L = 27. (Now we only have 2 variables, M and L).
Let’s look at the next part of the first sentence . . . “The longest side is 4 inches longer than 3 times the shortest side”
So, L = 4 + 3S
But, remember that S = M - 8 so we can rewrite this equation as
L = 4 + 3(M - 8) and then simplify . . .
L = 4 + 3M - 24
L = 3M - 20
If we replace L in our perimeter equation with 3M - 20, we will have
(M - 8) + M + 3M - 20 = 27 and then add like terms
5M - 28 = 27. Now add 28 to both sides
5M = 55. Now divide both sides by 5
M = 11.
The medium side is 11 inches. Use this to find the other sides.
S = M - 8 = 11 - 8 = 3 inches
L = 3M - 20 = 3(11) - 20 = 33 - 20 = 13 inches.
Notice that 3 + 11 + 13 = 27!!!
Hope this helps!
JMJ
