ACT Math : Plane Geometry
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Example Questions
Example Question #181 : Geometry
If the area of an isosceles triangle is 
Use the formula for area of a triangle to solve for the height:
Example Question #182 : Plane Geometry
Find the height of the isosceles triangle above if the length of 
Because this is an isosceles triangle, 
Thus we use the Pythagorean Theorem to find the length of the long arm:
Example Question #183 : Plane Geometry
The triangle above has an area of 
The area of a triangle is found using the formula
The height of any triangle is the length from it's highest point to the base, as pictured below:
We can find the height by rearranging the area formula:
Example Question #181 : Plane Geometry
The ratio of the side lengths of a triangle is 7:10:11. In a similar triangle, the middle side is 9 inches long. What is the length of the longest side of the second triangle?
9
10
9.9
7.7
12.1
9.9
Side lengths of similar triangles can be expressed in proportions. Establish a proportion comparing the middle and long sides of your triangles.
10/11 = 9/x
Cross multiply and solve for x.
10x = 99
x = 9.9
Example Question #181 : Act Math
Two triangles are similar to each other. The bigger one has side lengths of 12, 3, and 14.
The smaller triangle's shortest side is 1 unit in length. What is the length of the smaller triangle's longest side?
Because the triangles are similar, a ratio can be set up between the triangles' longest sides and shortest sides as such: 14/3 = x/1. Solving for x, we obtain that the shortest side of the triangle is 14/3 units long.
Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar
The ratio of the side lengths of a triangle is 
Use proportions to solve for the missing side:
Cross multiply and solve:
Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar
There are two similar triangles. One has side lengths of 14, 17, and 19. The smaller triangle's smallest side length is 2. What is the length of its longest side?
Use proportions to solve for the missing side:
Cross multiply and solve:
Example Question #182 : Geometry
A triangle has a perimeter of 36 inches, and one side that is 12 inches long. The lengths of the other two sides have a ratio of 3:5. What is the length of the longest side of the triangle?
8
12
15
9
14
15
We know that the perimeter is 36 inches, and one side is 12. This means, the sum of the lengths of the other two sides are 24. The ratio between the two sides is 3:5, giving a total of 8 parts. We divide the remaining length, 24 inches, by 8 giving us 3. This means each part is 3. We multiply this by the ratio and get 9:15, meaning the longest side is 15 inches.
Example Question #183 : Plane Geometry
What is the value of 
Cannot be computed
What is the value of 
Begin by filling in the missing angle for your triangle. Since a triangle has a total of 
Draw out the figure:
Now, to solve this, you will need some trigonometry. Use the Law of Sines to calculate the value:
Solving for 
Rounding, this is 
Example Question #3 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle
What is the value of 
Cannot be computed
Begin by filling in the missing angle for your triangle. Since a triangle has a total of 
Draw out the figure:
Now, to solve this, you will need some trigonometry. Use the Law of Sines to calculate the value:
Solving for 
Rounding, this is 
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