Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem: example 3.35

The perimeter of a triangular garden is 24 feet. The lengths of two sides are four feet and nine feet. How long is the third side?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

The perimeter of a triangular garden is 48 feet. The lengths of two sides are 18 feet and 22 feet. How long is the third side?

How did it go?

Step 1. Read the problem. Draw the figure and label it with the given information.
Step 2. Identify what you are looking for.	length of the third side of a triangle
Step 3. Name. Choose a variable to represent it.	Let $c =$ the third side.
Step 4. Translate.
Write the appropriate formula and substitute.
Substitute in the given information.
Step 5. Solve the equation.
Step 6. Check. $\begin{matrix} P & = & a + b + c \\ 24 & ≟ & 4 + 9 + 11 \\ 24 & = & 24 ✓ \end{matrix}$
Step 7. Answer the question.	The third side is 11 feet long.

Step 1. Read the problem. Draw the figure and label it with the given information.
Step 2. Identify what you are looking for.	length of the third side of a triangle
Step 3. Name. Choose a variable to represent it.	Let $c =$ the third side.
Step 4. Translate.
Write the appropriate formula and substitute.
Substitute in the given information.
Step 5. Solve the equation.
Step 6. Check. $\begin{matrix} P & = & a + b + c \\ 24 & ≟ & 4 + 9 + 11 \\ 24 & = & 24 ✓ \end{matrix}$
Step 7. Answer the question.	The third side is 11 feet long.