ACT Math : Plane Geometry
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Example Questions
Example Question #1 : How To Find The Perimeter Of A Rectangle
The length of a rectangle is 3 more inches than its width. The area of the rectangle is 40 in2. What is the perimeter of the rectangle?
34 in.
26 in.
40 in.
18 in.
None of the answers are correct
26 in.
Area of rectangle: A = lw
Perimeter of rectangle: P = 2l + 2w
w = width and l = w + 3
So A = w(w + 3) = 40 therefore w2 + 3w – 40 = 0
Factor the quadratic equation and set each factor to 0 and solve.
w2 + 3w – 40 = (w – 5)(w + 8) = 0 so w = 5 or w = -8.
The only answer that makes sense is 5. You cannot have a negative value for a length.
Therefore, w = 5 and l = 8, so P = 2l + 2w = 2(8) + 2(5) = 26 in.
Example Question #1 : How To Find The Perimeter Of A Rectangle
Kayla took 25 minutes to walk around a rectangular city block. If the block's width is 1/4 the size of the length, how long would it take to walk along one length?
2.5 minutes
7 minutes
8 minutes
10 minutes
10 minutes
Leaving the width to be x, the length is 4x. The total perimeter is 4x + 4x + x + x = 10x.
We divide 25 by 10 to get 2.5, the time required to walk the width. Therefore the time required to walk the length is (4)(2.5) = 10.
Example Question #3 : How To Find The Perimeter Of A Rectangle
The area of a rectangle is 
The area of a rectangle is the width times the height, and we are told that in this rectangle the width is two times the height.
Therefore, 
Plug in the value of the area:
Solve for 
Example Question #1 : How To Find The Perimeter Of A Rectangle
Robert is designing a rectangular garden. He wants the area of the garden to be 9 square meters. If the length of the lot is going to be three meters less than twice the width, what will the perimeter of the lot be in meters?
6
1.5
12
3
10
12
Let l be the length of the garden and w be the width.
By the specifications of the problem, l = 2w-3.
Plug this in for length in the area formula:
A = l x w = (2w - 3) x w = 9
Solve for the width:
2w²- 3w - 9 =0
(2w + 3)(w - 3) = 0
w is either 3 or -3/2, but we can't have a negative width, so w = 3.
If w = 3, then length = 2(3) - 3 = 3.
Now plug the width and length into the formula for perimeter:
P = 2 l + 2w = 2(3) + 2(3) = 12
Example Question #372 : Geometry
What is the perimeter of a rectangle with one side of 
Based on the information provided, you know that the rectangle's area could be represented as:
Now, remember that your perimeter is just the sum of all the sides. This is:
For our data, this is:
Example Question #373 : Geometry
The area of a yard is 
Begin by computing the length of the other side of the yard. Based on the data that you have, you know that:
Now, this means that our yard's dimensions in feet are:
The perimeter will be 
Example Question #374 : Geometry
A person spends 
Based on this data, you know that the person purchased a total of 
Solve the first equation for 
Now substitute this into the first equation:
Since this is a quadratic equation, isolate everything to one side:
This is a bit tricky to factor, but it comes out as:
This means that the larger dimension is 
Example Question #1 : How To Find The Perimeter Of A Rectangle
A rectangle has an area of 
To find the length and width of a rectangle given the area and one side, simply divide the area by the given side length:
Next, to find the perimeter use the formula:
Example Question #31 : Rectangles
Find the perimeter of a perimeter with width 5 and length 8.
To solve, simply use the formula for the perimeter of a rectangle. Thus,
Example Question #32 : Rectangles
Find the perimeter of a perimeter with width 5 and length 9.
To solve, simply use the formula for the perimeter of a rectangle. Thus,
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