Question 18 - review

Question

The perimeter of a triangle is 73 in. The longest side is 14 in. longer than the medium​ side, and the medium side is 4 in. more than the shortest side. Find the length of each side of the triangle.

The length of the longest side is_____ inches , the length of the medium side is ____ inches, and the length of the shortest side is _____ inches.

Answer 1

Hi Di,

The perimeter of a triangle is 73 in.

The longest side is 14 in. longer than the medium​ side,

and the medium side is 4 in. more than the shortest side.

Find the length of each side of the triangle.

The length of the longest side is_____ inches , the length of the medium side is ____ inches, and the length of the shortest side is _____ inches.

Given:

Triangle

Perimeter = 73in

Longest Side = 14 in longer than medium side

Medium side = 4 in more than shortest side

Find: Length of each side of the triangle

First we are told the perimeter is 73 in.

The Perimeter of a triangle is found by adding the length of all 3 sides.

We have a long, medium, and short side.

Let L = long side

M = Medium Side

S = Short side.

We can generate equations from the relationships given

Longest Side = 14 in longer than medium side

L = M + 14in

Medium side = 4 in more than shortest side

M = 4 in + S

Solve this one for S

M-4in = S

Perimeter = L + M + S = 73in

(M + 14in) + M + (M - 4in) = 73 in

3M +10in = 73in

3M = 63

M = 21

L = M +14in, L=21 + 14 = 35

S = M-4in S = 21-4 = 17

We can check to make sure we solved correctly.

L+M+S ?= 73in

35 + 21 + 17 ?= 73

73 = 73

The answer checks out.

Hope this helps!

Let me know if you have anymore questions :)