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Find the area of a triangle with base $13$ inches and height $2$ inches.
13 sq. in.
Find the area of a triangle with base $14$ inches and height $7$ inches.
49 sq. in.
The perimeter of a triangular garden is $24$ feet. The lengths of two sides are $4$ feet and $9$ feet. How long is the third side?
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. Substitute in the given information. 

Step 5. Solve the equation.  
Step 6.
Check:


Step 7. Answer the question.  The third side is 11 feet long. 
The perimeter of a triangular garden is $24$ feet. The lengths of two sides are $18$ feet and $22$ feet. How long is the third side?
8 ft
The lengths of two sides of a triangular window are $7$ feet and $5$ feet. The perimeter is $18$ feet. How long is the third side?
6 ft
The area of a triangular church window is $90$ square meters. The base of the window is $15$ meters. What is the window’s height?
Step 1. Read the problem. Draw the figure and label it with the given information.  
Step 2. Identify what you are looking for.  height of a triangle 
Step 3. Name. Choose a variable to represent it.  Let h = the height 
Step 4.
Translate.
Write the appropriate formula. Substitute in the given information. 

Step 5. Solve the equation.  
Step 6.
Check:


Step 7. Answer the question.  The height of the triangle is 12 meters. 
The area of a triangular painting is $126$ square inches. The base is $18$ inches. What is the height?
14 in.
A triangular tent door has an area of $15$ square feet. The height is $5$ feet. What is the base?
6 ft
Besides the right triangle, some other triangles have special names. A triangle with two sides of equal length is called an isosceles triangle . A triangle that has three sides of equal length is called an equilateral triangle . [link] shows both types of triangles.
An isosceles triangle has two sides the same length.
An equilateral triangle has three sides of equal length.
The perimeter of an equilateral triangle is $93$ inches. Find the length of each side.
Step 1. Read the problem. Draw the figure and label it with the given information. 
Perimeter = 93 in. 
Step 2. Identify what you are looking for.  length of the sides of an equilateral triangle 
Step 3. Name. Choose a variable to represent it.  Let s = length of each side 
Step 4.
Translate.
Write the appropriate formula. Substitute. 

Step 5. Solve the equation.  
Step 6.
Check:


Step 7. Answer the question.  Each side is 31 inches. 
Find the length of each side of an equilateral triangle with perimeter $39$ inches.
13 in.
Find the length of each side of an equilateral triangle with perimeter $51$ centimeters.
17 cm
Arianna has
$156$ inches of beading to use as trim around a scarf. The scarf will be an isosceles triangle with a base of
$60$ inches. How long can she make the two equal sides?
Step 1. Read the problem. Draw the figure and label it with the given information. 
P = 156 in. 
Step 2. Identify what you are looking for.  the lengths of the two equal sides 
Step 3. Name. Choose a variable to represent it.  Let s = the length of each side 
Step 4.
Translate.
Write the appropriate formula. Substitute in the given information. 

Step 5. Solve the equation.  
Step 6.
Check:


Step 7. Answer the question.  Arianna can make each of the two equal sides 48 inches long. 
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