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
