ACT Math : Quadrilaterals
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Example Questions
Example Question #121 : Quadrilaterals
Find the area of rectangle given width of 5 and length of 8.
To solve, simply use the formula for the area of a rectangle. Thus,
Example Question #122 : Quadrilaterals
Erin is getting ready to plant her tulip garden. She wants to plant two tulips per square foot of garden. If her rectangular garden is enclosed by 24 feet of fencing, and the length of the fence is twice as long as its width, how many tulips will Erin plant?
64
24
32
48
16
64
We know that the following represents the formula for the perimeter of a rectangle:
In this particular case, we are told that the length of the fence is twice as long as the width. We can write this as the following expression:
Use this information to substitute in a variable for the length that matches the variable for width in our perimeter equation.
We also know that the length is two times the width; therefore, we can write the following:
The area of a rectangle is found by using this formula:
The area of the garden is 32 square feet. Erin will plant two tulips per square foot; thus, she will plant 64 tulips.
Example Question #2 : How To Find The Length Of The Diagonal Of A Rectangle
A rectangle has a height of 
1. Use Pythagorean Theorem with 
2. Solve for 
This rounds down to 
Example Question #1 : 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 #1 : How To Find The Length Of The Diagonal Of A Rectangle
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 #125 : Quadrilaterals
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 #126 : Quadrilaterals
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 #1 : 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 = 1/3l +2
w = 3l – 2
w = 6l +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
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