Math Snap

STEP 1

What is this asking?
We need to find the lengths of the three sides of a triangle when we know the total length around the triangle and how the side lengths relate to each other.
Watch out!
Don't forget that the perimeter is the sum of all sides!
Also, make sure to clearly define what your variables represent to avoid confusion.

STEP 2

1. Set up variables and equations
2. Solve for the first side
3. Calculate other sides

STEP 3

Let's define our variables!
We'll call the length of the first side $x$.
Since the second side is three times as long as the first side, we can represent its length as $3x$.
The third side is 5 m shorter than the second side, so its length is $3x - 5$.

STEP 4

Now, let's build our equation!
We know the perimeter is the sum of all the sides, and it's given as 107 m.
So, we can write the equation: $x + 3x + (3x - 5) = 107$.
This equation says the sum of the lengths of the three sides equals the perimeter.

STEP 5

Let's simplify our equation!
Combining the $x$ terms, we get $7x - 5 = 107$.

STEP 6

To isolate the $x$ term, we'll add 5 to both sides of the equation: $7x - 5 + 5 = 107 + 5$, which simplifies to $7x = 112$.
We're adding 5 to both sides to make the left side simpler.

STEP 7

Now, we'll divide both sides by 7 to solve for $x$: $\frac{7x}{7} = \frac{112}{7}$.
This gives us $x = 16$.
So, the length of the first side is 16 m!
We divide by 7 to turn the $7x$ into a single $x$.

STEP 8

We know the second side is three times the length of the first side, so it's $3 \cdot 16 = 48$.
The second side is 48 m long!

STEP 9

The third side is 5 m shorter than the second side, so it's $48 - 5 = 43$.
The third side is 43 m long!

The lengths of the sides are:
First side: 16 m
Second side: 48 m
Third side: 43 m