How to find the length of an edge of a prism - ACT Math

When reading word problems, there are certain clues that help interpret what is going on. The word “is” generally means “=” and the word “times” means it will be multiplied by something. Therefore, “the length of a box is 3 times the width” gives you the answer: L = 3 x W, or L = 3W.

We notice the width is “5 inches less than three times its width,” so we express W as being three times its width (3L) and 5 inches less than that is 3L minus 5. In this case, W is the dependent and L is the independent variable.

W = 3L - 5

This sounds like a geometry problem, so start by drawing a picture so that you know exactly what you are dealing with.

Because we are dealing with rectangular prisms and volume, we will need the following formula:

Or

We are solving for height, so you can begin by rearranging the equation to get by itself:

Then, plug in our knowns (, and )

Here is the problem worked out with a corresponding picture:

The trickiest part of this question is the wording. This problem is asking for the height of the water in the exhibit if the exhibit is three-quarters full. We can find this at least two different ways.

1. The longer way requires that we begin by finding three quarters of the total volume:

Now we go back to our volume equation, and since we are again looking for height, we want it solved for :

Becomes

1. The easier way requires that we recognize a key detail. If we take three-quarters of the volume without changing our length or width, our new height will just be three-quarters of the total height. We can solve for the total height of the exhibit by using the volume equation and rearranging it to solve for :

At this point, we can substitute in our given values and solve for :

So, the total height of the exhibit is . We can now easily solve for three-quarters of the total height:

When reading word problems, there are certain clues that help interpret what is going on. The word “is” generally means “=” and the word “times” means it will be multiplied by something. Therefore, “the length of a box is 3 times the width” gives you the answer: L = 3 x W, or L = 3W.

We notice the width is “5 inches less than three times its width,” so we express W as being three times its width (3L) and 5 inches less than that is 3L minus 5. In this case, W is the dependent and L is the independent variable.

W = 3L - 5

This sounds like a geometry problem, so start by drawing a picture so that you know exactly what you are dealing with.

Because we are dealing with rectangular prisms and volume, we will need the following formula:

Or

We are solving for height, so you can begin by rearranging the equation to get by itself:

Then, plug in our knowns (, and )

Here is the problem worked out with a corresponding picture:

The trickiest part of this question is the wording. This problem is asking for the height of the water in the exhibit if the exhibit is three-quarters full. We can find this at least two different ways.

1. The longer way requires that we begin by finding three quarters of the total volume:

Now we go back to our volume equation, and since we are again looking for height, we want it solved for :

Becomes

1. The easier way requires that we recognize a key detail. If we take three-quarters of the volume without changing our length or width, our new height will just be three-quarters of the total height. We can solve for the total height of the exhibit by using the volume equation and rearranging it to solve for :

At this point, we can substitute in our given values and solve for :

So, the total height of the exhibit is . We can now easily solve for three-quarters of the total height:

When reading word problems, there are certain clues that help interpret what is going on. The word “is” generally means “=” and the word “times” means it will be multiplied by something. Therefore, “the length of a box is 3 times the width” gives you the answer: L = 3 x W, or L = 3W.

We notice the width is “5 inches less than three times its width,” so we express W as being three times its width (3L) and 5 inches less than that is 3L minus 5. In this case, W is the dependent and L is the independent variable.

W = 3L - 5

This sounds like a geometry problem, so start by drawing a picture so that you know exactly what you are dealing with.

Because we are dealing with rectangular prisms and volume, we will need the following formula:

Or

We are solving for height, so you can begin by rearranging the equation to get by itself:

Then, plug in our knowns (, and )

Here is the problem worked out with a corresponding picture:

The trickiest part of this question is the wording. This problem is asking for the height of the water in the exhibit if the exhibit is three-quarters full. We can find this at least two different ways.

1. The longer way requires that we begin by finding three quarters of the total volume:

Now we go back to our volume equation, and since we are again looking for height, we want it solved for :

Becomes

1. The easier way requires that we recognize a key detail. If we take three-quarters of the volume without changing our length or width, our new height will just be three-quarters of the total height. We can solve for the total height of the exhibit by using the volume equation and rearranging it to solve for :

At this point, we can substitute in our given values and solve for :

So, the total height of the exhibit is . We can now easily solve for three-quarters of the total height:

When reading word problems, there are certain clues that help interpret what is going on. The word “is” generally means “=” and the word “times” means it will be multiplied by something. Therefore, “the length of a box is 3 times the width” gives you the answer: L = 3 x W, or L = 3W.

We notice the width is “5 inches less than three times its width,” so we express W as being three times its width (3L) and 5 inches less than that is 3L minus 5. In this case, W is the dependent and L is the independent variable.

W = 3L - 5

This sounds like a geometry problem, so start by drawing a picture so that you know exactly what you are dealing with.

Because we are dealing with rectangular prisms and volume, we will need the following formula:

Or

We are solving for height, so you can begin by rearranging the equation to get by itself:

Then, plug in our knowns (, and )

Here is the problem worked out with a corresponding picture:

The trickiest part of this question is the wording. This problem is asking for the height of the water in the exhibit if the exhibit is three-quarters full. We can find this at least two different ways.

1. The longer way requires that we begin by finding three quarters of the total volume:

Now we go back to our volume equation, and since we are again looking for height, we want it solved for :

Becomes

1. The easier way requires that we recognize a key detail. If we take three-quarters of the volume without changing our length or width, our new height will just be three-quarters of the total height. We can solve for the total height of the exhibit by using the volume equation and rearranging it to solve for :

At this point, we can substitute in our given values and solve for :

So, the total height of the exhibit is . We can now easily solve for three-quarters of the total height:

When reading word problems, there are certain clues that help interpret what is going on. The word “is” generally means “=” and the word “times” means it will be multiplied by something. Therefore, “the length of a box is 3 times the width” gives you the answer: L = 3 x W, or L = 3W.

We notice the width is “5 inches less than three times its width,” so we express W as being three times its width (3L) and 5 inches less than that is 3L minus 5. In this case, W is the dependent and L is the independent variable.

W = 3L - 5

This sounds like a geometry problem, so start by drawing a picture so that you know exactly what you are dealing with.

Because we are dealing with rectangular prisms and volume, we will need the following formula:

Or

We are solving for height, so you can begin by rearranging the equation to get by itself:

Then, plug in our knowns (, and )

Here is the problem worked out with a corresponding picture:

The trickiest part of this question is the wording. This problem is asking for the height of the water in the exhibit if the exhibit is three-quarters full. We can find this at least two different ways.

1. The longer way requires that we begin by finding three quarters of the total volume:

Now we go back to our volume equation, and since we are again looking for height, we want it solved for :

Becomes

1. The easier way requires that we recognize a key detail. If we take three-quarters of the volume without changing our length or width, our new height will just be three-quarters of the total height. We can solve for the total height of the exhibit by using the volume equation and rearranging it to solve for :

At this point, we can substitute in our given values and solve for :

So, the total height of the exhibit is . We can now easily solve for three-quarters of the total height: