3.4 Solve geometry applications: triangles, rectangles, and the  (Page 4/8)

Solution

Step 1. Read the problem.
Step 2. Identify what you are looking for.	the length of the hypotenuse of the triangle
Step 3. Name. Choose a variable to represent it. Label side c on the figure.	Let c = the length of the hypotenuse.
Step 4. Translate.
Write the appropriate formula.	$a^2+b^2=c^2$
Substitute.	$3^2+4^2=c^2$
Step 5. Solve the equation.	$9+16=c^2$
Simplify.	$25=c^2$
Use the definition of square root.	$\sqrt{25}=c$
Simplify.	$5=c$
Step 6. Check.
Step 7. Answer the question.	The length of the hypotenuse is 5.

Solution

Step 1. Read the problem.
Step 2. Identify what you are looking for.		the length of the leg of the triangle
Step 3. Name. Choose a variable to represent it.		Let b = the leg of the triangle.
Lable side b .
Step 4. Translate
Write the appropriate formula.		$a^2+b^2=c^2$
Substitute.		$5^2+b^2={13}^2$
Step 5. Solve the equation.		$25+b^2=169$
Isolate the variable term.		$b^2=144$
Use the definition of square root.		$b^2=\sqrt{144}$
Simplify.		$b=12$
Step 6. Check.
Step 7. Answer the question.		The length of the leg is 12.

Solution

$\begin{array}{cccc}\mathbf{\text{Step 1.}}\text{Read the problem.}\hfill & & & \\ \mathbf{\text{Step 2.}}\text{Identify what we are looking for.}\hfill & & & \begin{array}{c}\text{the distance from the corner that the}\hfill \\ \text{bracket should be attached}\hfill \end{array}\hfill \\ \\ \\ \mathbf{\text{Step 3.}}\text{Name. Choose a variable to represent it.}\hfill & & & \text{Let}x=\text{the distance from the corner.}\hfill \\ \\ \\ \begin{array}{c}\mathbf{\text{Step 4.}}\text{Translate.}\hfill \\ \text{Write the appropriate formula and substitute.}\hfill \\ \\ \\ \mathbf{\text{Step 5.}}\text{Solve the equation.}\hfill \\ \\ \text{Isolate the variable.}\hfill \\ \text{Use the definition of square root.}\hfill \\ \text{Simplify. Approximate to the nearest tenth.}\hfill \end{array}\hfill & & & \hfill \begin{array}{}\\ \hfill a^2+b^2& =\hfill & c^2\hfill \\ \hfill x^2+x^2& =\hfill & {10}^2\hfill \\ \\ \\ \hfill 2x^2& =\hfill & 100\hfill \\ \hfill x^2& =\hfill & 50\hfill \\ \hfill x& =\hfill & \sqrt{50}\hfill \\ \hfill x& \approx \hfill & 7.1\hfill \end{array}\hfill \\ \mathbf{\text{Step 6.}}\text{Check.}\hfill & & & \\ \begin{array}{ccc}\hfill a^2+b^2& =\hfill & c^2\hfill \\ \hfill {(7.1)}^2+{(7.1)}^2& \approx \hfill & {10}^2\text{Yes.}\hfill \end{array}\hfill & & & \\ \mathbf{\text{Step 7.}}\text{Answer the question.}\hfill & & & \begin{array}{c}\text{Kelvin should fasten each piece of}\hfill \\ \text{wood approximately}7.1\text{″}\text{from the corner.}\hfill \end{array}\hfill \end{array}$