Question

The longest side of a triangle is six more units than the shortest side. The third side is twice the length of the shortest side. If the perimeter of the triangle is 26 units, write and solve an equation to fine the lengths of all three sides of the triangle.

Answer 1

The perimeter is the total of adding all of the side lengths together.

s = shortest side

L = longest side

T = third side

L = s + 6  (longest side is 6 more units than the shortest side)

T = 2s  (the third side is twice the length of the shortest side)

Equation is:

P = s + L + T

You can plug in the equations of L = s + 6 and T = 2s into "L" and "T":

P = s + L + T

P = s + (s + 6) + (2s)      You know the perimeter is 26, so you can plug it into P

26 = s + s + 6 + 2s

26 = 2s + 6 + 2s

26 = 4s + 6  

20 = 4s

5 = s

Now that you know s, you can plug it into L = s + 6 and T = 2s

L = s + 6

L = 5 + 6

L = 11

T = 2s

T = 2(5)

T = 10

The shortest side is 5 units, the longest side is 11 units, the third side is 10 units