Question

The perimeter of a triangle is 84 feet. Find the length of the three sides if the middle length side is 5 feet greater than twice the length of the smallest side, and the longest side is 5 feet les than 3 times the length of the smallest side?

Answer 1

Answer: Smaller side = 14ft

middle side = 33ft

Larger side = 37ft

Step-by-step explanation:

This triangle has 3 sides, defined by the variables:

S = length of the smallest side.

M = length of the middle side.

L = length of the larger side.

And the perimeter of a triangle is equal to the addition of the length of each side of the triangle.

We also know that:

M = 5ft + 2*S

L = 3*S - 5ft

84ft = S + M + L.

The first step is to replace the first and the second equation into the third, so we can solve it for S.

84ft = S + (5ft + 2*S) + (3*S - 5ft)

84ft = 6*S

84ft = 6*S

84ft/6 = 14ft = S.

Now that we found the length of the shorter side, we can replace it in the above equations to find the length of the other two sides:

M = 5ft + 2*S = 5ft + 2*14ft = 33ft

L = 3*S - 5ft = 37ft