Let's create a similar triangle to the one with a perimeter of 76 inches. I'll call the original Triangle A, and the similar one that we are creating, Triangle B.
So, we are going to assign the lengths of Triangle B as 2, 8, and 9, which will make its perimeter 19.
Then, we can set up proportions to solve, which will give us the lengths of Triangle A's sides.
Length of shortest side (in. ) of Triangle B Length of shortest side (in.) of Triangle A
___________________________________ = ___________________________________
Perimeter (in.) of Triangle B Perimeter (in.) of Triangle A
Next, we fill in the known quantities to get the following proportion. I'll use x for the length unknown side.
2 x
____ = _____
19 76
Cross-multiply to get:
19x = (2)(76)
19x = 152
Divide each side by 19 to get:
x = 8
One side of the original triangle is 8 inches long.
I will not do your entire triangle, but I will set up a second proportion for you and let you finish this homework problem yourself. I will use z for the length of the side of the longest side of Triangle A.
Length of longest side (in. ) of Triangle B Length of longest side (in.) of Triangle A
___________________________________ = ___________________________________
Perimeter (in.) of Triangle B Perimeter (in.) of Triangle A
