MAC1105 practice question 114

Question

The perimeter of a triangle is 62 in. The longest side is 14 in. longer than the medium​ side, and the medium side is 6 in. more than the shortest side. Find the length of each side of the triangle.

The length of the longest side is ____________________., the length of the medium side is ___________. and the length of the shortest side is _________.

Answer 1

Let:

-- l be the length of the longer side

-- m be the length of the medium side

-- s be the length of the shorter side

l = 14 + m --> Longer side is 14 inches more than medium side

m = 6 + s --> m - 6 = s <-- Medium side is 6 inches more than shorter side

l + m + s = 62 <-- Perimeter of triangle

(14+m) + m + (m-6) = 62

3m + 8 = 62

3m = 54

m = 18

l = 14 + m

l = 14 + 18

l = 32

l + m + s = 62

32 + 18 + s = 62

50 + s = 62

s = 12

Therefore, the longer side is 32 inches, the medium side is 18 inches, and the shorter side is 12 inches, however, the sum of the shorter and medium sides are not greater than the longer side of 32 inches, so this triangle can't exist.