The perimeter of is 108 in. Find the lengths of the sides.
A) 24 in., 36 in., 96 in.
B) 24 in., 36 in., 48 in.
C) 26 in., 39 in., 48 in.
D) 24 in., 36 in., 60 in.
E) 26 in., 39 in., 52 in.

Question

The perimeter of  is 108 in. Find the lengths of the sides. ​  ​
A) 24 in., 36 in., 96 in. 
B) 24 in., 36 in., 48 in. 
C) 26 in., 39 in., 48 in. 
D) 24 in., 36 in., 60 in. 
E) 26 in., 39 in., 52 in.

Quizplus · Accepted Answer

Let the sides of the triangle be x, y, and z. Then we have:
x + y + z = 108 in.
But we also know that a triangle with sides x, y, and z has perimeter P = x + y + z.
Therefore, we have P = 108 in. and x + y + z = P.
Substituting P for 108 in. gives x + y + z = 108 in.
Since we are given that the sides have integer lengths, we can try to solve for x, y, and z using trial and error or by finding factors of 108. The only answer choice that satisfies this is (B):
24 in., 36 in., 48 in.
24 + 36 + 48 = 108

The Perimeter of Is 108 In