If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Basic geometry and measurement>Unit 13

Lesson 3: Pythagorean theorem application

# Pythagorean theorem word problem: carpet

If we draw the diagonal on a rectangular carpet, then its length, width, and diagonal form a right triangle. Since we know the length and diagonal measurements, we can use the Pythagorean theorem to solve for the missing width of the carpet. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• what is meant by diagonal?
• Draw a rectangle.
Draw a line that splits the rectangle into two triangles.
That line is a diagonal.
Focus on one of the triangles.
Notice that the triangle is a right triangle.
You will find that the diagonal is the longest line in the triangle.

(The definition of a diagonal is a line that connects two nonconsecutive vertices of a polygon.)
• i have never seen the way he regrouped the numbers while subtracting. (at ) how did he do that?
• Why cant you get a real value amount for the equation instead of a square root
• When we have perfect squares, then square roots are easy. It is when we have imperfect squares such as 2,3,5 etc. that it gets more complicated. When taking imperfect squares, we end up in a part of numbers called irrational numbers - numbers that cannot be expressed as a fraction of two integers (thus are non-repeating). sqrt(2) is a real number, but it is also an irrational number and thus cannot be expressed in the way you want.
However, for most real world problems, we can round an irrational number (like when we use 3.14 to approximate pi) to assist in calculations. However, anytime that we round, we loose accuracy, so sqrt(2) is more accurate than 1.414, so in Math which is can be more theoretical than real life, we just leave the sqrt(2) alone.
• what do you do when you have to find out for B?
• Rearrange the formula (a2+b2=c2) to isolate b: (c2-a2=b2). Now you can solve for b the same way you would for c. :)
• Would it be possible (if so is it easier?), if we made the equation as W²= (√74)²-7². Because technically it is the same thing right??
• That is technically right, but skipping steps can confuse you later on.
(1 vote)
• Can you break (√74)² down for me in steps? How do you solve that?
• This is really just a one-step problem. The squaring undoes the process of taking the square root, so the answer is just 74.
• Why do they always make the videos and why can't they make a written version that isn't just the video's script, is it too much work or something.
• Well, the videos help visual learners more than just a written version, especially with geometry as you really can't get a grasp of some concepts without it being drawn out. In addition to videos, Khan Academy also has some articles scattered throughout the site. To answer your question: Yes, it would be too much work, because the limited KA team is spending effort reproducing already existing content instead of making new content.
• What is this theory?
• Pythagorean Theorem.
• In "Pythagorean theorem word problems" quiz there is an inscribed triangle question giving a result that requires you to find the square root of 4.5√. And find a result of: 2.121. Fair enough, but I can't figure out how to find the square root of a decimal number. Can anyone help me to understand it?
• You could factor the √4.5 as √9 * √(1/2) which leaves you with (3√2)/2 but if you want a decimal answer there is certainly nothing wrong with just using your calculator when presented with something like that.
• In the solution to the following pyramid problem there
is a step, I do not understand.