the length of the shortest? side, the third side is 30 feet more than the length of the shortest side. Find the dimensions if the perimeter is 146 feet.

Question

A flower bed is in the shape of a triangle with one side twice the length of the shortest? side, and the third side is
30 feet more than the length of the shortest side. Find the dimensions if the perimeter is 146 feet.

Answer 1

Hi Savannah, the perimeter of a triangle is the some of the sides. Let S represent the shortest side. Then the second side is 2S since it is twice as long as the shortest side. Last, the third side is S + 30 since it is 30 feet longer than the shortest side.

 

Equation:

 

P = S₁ + S₂ + S₃

 

Substituting:

 

P = 146 feet

 

S₁ = S

 

S₂ = 2S

 

S₃ = S + 30

 

S + 2S + S + 30 = 146

 

4S + 30 = 146

 

Subtract 30 from both sides:

 

4S = 116

 

Divide both sides by 4:

 

S = 29

 

Solution:

 

The shortest side of the triangle is 29 feet.

 

The second side is twice the length of the shortest side, or 2 * 29 = 58 feet.

 

The third side is 30 feet longer than the shortest side, or 29 + 30 = 59 feet.

 

Questions?