131k views
2 votes
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.

User MrChaz
by
7.2k points

1 Answer

3 votes

Answer:

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.

User Peter Meinl
by
7.8k points