Question

One side of a triangle is twice the shortest side. The third side is five feet more than the shortest side. The perimeter is 17 feet. Find the lengths of all three sides.

Answer 1

3, 6 and 8

Explanation:

In order to solve the problem, we call:

`a` = length of the 1st side of the triangle

`b` = length of the 2nd side of the triangle

`c` = length of the 3rd side of the triangle

From the text of the question, we know that:

- One side of a triangle is twice the shortest side --> we can write this as

`b=2a` (1) (assuming "a" is the shortest side)

- The third side is five feet more than the shortest side. -->

`c=a+5` (2)

- The perimeter is 17 feet -->

`a+b+c=17` (3)

So now we have 3 equations with 3 unknown variables. Substituting (1) and (2) into (3) we can find the value of "a", the shortest side:

`a+2a+a+5=17\\4a=17-5=12\\a=3`

And so

`b=2\cdot 3=6\\c=3+5=8`

So the lengths of the 3 sides are 3, 6 and 8.