What is the length of the diagonal of a rectangular box with the dimensions of ?
Possible Answers: Correct answer: Explanation :To solve this problem we need an extension of the Pythagorean Theorem:
So the equation to solve becomes
So the distance of the diagonal is .
Find the diagonal of the prism. The diagonal is represented by the dashed line.
The length of the diagonal is from the bottom left hand corner closest to us to the top right hand corner that's farthest away from us.
This kind of a problem may seem to be a little more complicated than it really is.
In order to solve for the diagonal length, all that's required is the Pythagorean Theorem. This equation will be used twice to solve for the dashed line.
For the first step of this problem, it's helpful to imagine a triangle "slice" that's being taken inside the prism.
, where the diagonal of interest is D2, and D1 is the diagonal that cuts from corner to corner of the bottom face of the prism. Of this triangle that's outlined in pink dashed lines, the given information (the dimensions of the prism) provides a length for one of the legs (16).
We can already "map out" that D2 (the hypotenuse of the dashed triangle) can be solved by using the Pythagorean Theorem if we can obtain the length of the other leg (D1).
The next step of this problem is to solve for D1. This will be the first use of the Pythagorean theorem. D1 is the diagonal of the base and is limited to a 2D face. This can be represented as:
The hypotenuse of the base, or the mystery length leg of the dashed triangle, can be solved by using the Pythagorean Theorem:
Now that we calculated the length of D1, D2 can be solved for by using the Pythagorean Theorem a second time:
A right rectangular prism has a width of cm, a length of cm, and a height of cm. Find the diagonal distance of the prism.
Possible Answers:None of the other answers.
Correct answer: Explanation :To find the diagonal distance of a prism, you can use the formula:
, where = height; = width, and = length.
So, in this problem
A right rectangular prism has a height of ft, a width of feet and a length that is twice its width. The volume of the prism is cubic feet. What is the diagonal of the prism?
Possible Answers:None of the other answers.
Correct answer: Explanation :First, given the volume, you need to find the width and length. The volume of a right, rectangular prism can be found using
, so , where represents the length and represents the width.
Solving for , you get
So, the width of the prism is 3 feet.
Remember that the length is twice the width, so the length is 6 feet.
Now you may use the formula for finding the diagonal:
A right, rectangular prism has a length of meters, width that is meters longer than the length, and a height of meters. The volume of the prism is cubic meters. Find the diagonal of the prism.
Possible Answers:None of the other answers.
Correct answer: Explanation :First, use the volume formula,
to find the missing length and width.
Since cannot be a negative value is it represents a length of a prism, we know . So the length is 2 meters, and therefore the width is 5 meters.
Now you can plug in the length, width and height into the formula for finding the diagonal of the prism.
A right, rectangular prism has a volume of cubic centimeters. Its width is cm and its length is three times its height. Find the length of the diagonal of the prism.
Possible Answers:None of the other answers.
Correct answer: Explanation :First, use the volume to find the missing height and length.
Since the length is three times the height, use to represent the length and to represent the height.
So the height of the prism is 2 centimeters, and the length is 6 centimeters.
Use these values to now solve for the diagonal distance.
The surface area of a right, rectangular prism is square inches. The height is inches and the length is times the width. Find the diagonal distance of the prism.
Possible Answers:None of the other choices.
Correct answer: Explanation :Use the surface area, 280 square inches, and the formula for finding the surface area of a right, rectangular prsim to find the missing length and width measurements.
Since represents the length of a solid figure, we must assume , rather than the negative value.
So, the width of the figure is 2 inches and the length is 10 inches.
Now, use the formula for finding the diagonal of a right, rectangular prism:
A right, rectangular prism has a surface area of square meters. Its width is twice its length, and its height is four times its length. Find the diagonal distance of the prism.
Possible Answers:None of the other answers.
Correct answer: Explanation :Use the surface area of the prism to find the missing length, width and height.
So, the prism's length is 1 meter, the width is 2 meters and the height is 4 meters.
Now you can find the diagonal distance using those values.
The above cube has edges of length 1. True or false: The dashed line has length .
Possible Answers: Correct answer: Explanation :Examine the diagram below.
is a right triangle with legs of length , so it is an isosceles - or 45-45-90 - right triangle. By the 45-45-90 Triangle Theorem its hypotenuse measures
is a right triangle with legs of lengths and , so the length of its hypotenuse is
, the diagonal in question, has length , not .
Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil.
Military Technical College, Bachelor of Engineering, Telecommunications Engineering. Military Technical College, Master of Sc.
If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources.
If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.
Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.
Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.
Please follow these steps to file a notice:
You must include the following:
A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.
Send your complaint to our designated agent at:
Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105
Or fill out the form below:
