ACT Math : Plane Geometry
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Example Questions
Example Question #4 : How To Find The Length Of The Diagonal Of A Rectangle
The sides of rectangle ABCD are 4 in and 13 in.
How long is the diagonal of rectangle ABCD?
A diagonal of a rectangle cuts the rectangle into 2 right triangles with sides equal to the sides of the rectangle and with a hypotenuse that is the diagonal. All you need to do is use the pythagorean theorem:
Example Question #123 : Quadrilaterals
A power company needs to run a piece of wire across a rectangular plot of land and must do so diagonally. The land is 
Notice that this problem could be represented as follows:
This means that you can find the distance of the wire merely by using the Pythagorean theorem:
Solving for 
Thus,
Using your calculator, multiply this by 
Example Question #123 : Quadrilaterals
What is the diagonal of a rectangle with sides of length 
You could draw this rectangle as follows:
Solving for the diagonal merely requires using the Pythagorean theorem. Thus, you know:
This is approximately 
Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle
What is the area of a rectangle with a diagonal of 
Based on the description offered in the question, you know that your rectangle must look something like this:
Using the Pythagorean theorem, you can solve for the unknown side 
Thus, 
Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle
Mark bought a TV at the store that was listed as 36in x 24in. He needs to figure out the diagonal to make sure the television is large enough but he left his measuring tape at his mother's house. What is the diagonal length of this television's screen in terms of inches?
Finding the diagonal of a rectangle is essentially a problem with triangles. If we set up a right triangle with legs 24 in. and 36 in., and set 
This comes out to be about 43.3 in.
Example Question #1 : How To Find The Length Of The Side Of A Rectangle
The width, in cm, of a rectangular fence is 2 more than half its length, in cm. Which of the following gives the width, w cm, in terms of length, l cm, of the rectangular fence?
w = ½ l – 2
w = ½ l + 2
w = 2l + 2
w = 2l – 2
w = ½ l + 2
To find the width, we must take half of the length, which means we must divide the length by 2. Then we must take 2 more than that number, which means we must add 2 to the number. Combining these, we get:
w = ½ l + 2
Example Question #2 : How To Find The Length Of The Side Of A Rectangle
The width of a rectangle is 2 inches longer than 3 times its length. Which of the following equations gives the width, w, of the rectangle in terms of its length, l,?
w = 6l +2
w = 3l – 2
w = 1/3l +2
w = 3l + 2
w = 3l + 2
The width equals 3 times the length, so 3l, plus an additional two inches, so + 2, = 3l + 2
Example Question #3 : How To Find The Length Of The Side Of A Rectangle
Your dad shows you a rectangular scale drawing of your house. The drawing is 6 inches by 8 inches. You're trying to figure out the actual length of the shorter side of the house. If you know the actual length of the longer side is 64 feet, what is the actual length of the shorter side of the house (in feet)?
81
48
32
36
60
48
We can solve this by setting up a proportion and solving for x,the length of the shorter side of the house. If the drawing is scale and is 6 : 8, then the actual house is x : 64. Then we can cross multiply so that 384 = 8x. We then divide by 8 to get x = 48.
Example Question #1 : How To Find The Perimeter Of A Rectangle
What is the perimeter of the below rectangle in simplest radical form?
5√3
10√3
4√3 + 2√27
7√27
10√3
The perimeter of a figure is the sum of the lengths of all of its sides. The perimeter of this figure is √27 + 2√3 + √27 + 2√3. But, √27 = √9√3 = 3√3 . Now all of the sides have the same number underneath of the radical symbol (i.e. the same radicand) and so the coefficients of each radical can be added together. The result is that the perimeter is equal to 10√3.
Example Question #2 : How To Find The Perimeter Of A Rectangle
A rectangle has an area of 56 square feet, and a width of 4 feet. What is the perimeter, in feet, of the rectangle?
Divide the area of the rectangle by the width in order to find the length of 14 feet. The perimeter is the sum of the side lengths, which in this case is 14 feet + 4 feet +14 feet + 4 feet, or 36 feet.
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