The longest side if a triangle is nine meters longer than the shortest side.

The other side is twice the length of the shortest side.

The perimeter of the triangle is 25 m.

Solve for all three sides

Probably good to start by sketching a diagram.

Then set up an algebraic expression for each statement in the problem.

Translate the words into separate equations (using all of the information given)

1. The longest side if a triangle is six units more than the shortest side

2. The other is twice the length of the shortest side

3. P=25

The part that I see come up more than once in the description is the shortest side.

The length of the longest side is described in terms of the shortest side and the length of the second longest side is also described in terms of the shortest side.

You could potentially use more variables, but it’s better to use the least number of variables possible to reduce the work necessary.

Therefore I’ll describe the sides of the triangle (from shortest to longest) as

1. x

2. 2x

3. x + 9

Then we can combine all the equations to solve because we know the perimeter.

x + 2x + x + 9 = 25

The next step is to combine like terms

4x + 9 = 25

After that we will subtract nine from both sides of the equation to isolate the variable.

4x = 16

Then divide each side by four to get x.

x = 16/4 = 4

Once we have x, we can substitute into the three equations to get all three side lengths

1. x

2. 2x

3. x + 9

1. 4

2. 8

3. 13

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