What is the pythagorean theorem?

timer Asked: Sep 18th, 2014
account_balance_wallet $5

Question Description

Explain what the theorem is and show an example of how it can be applied.

Tutor Answer

School: Cornell University

The pythagorean theorem is a formula relating the sides of a right triangle derived by a Greek mathematician named Pythagorus in the 500s BC. The formula works for all right triangles with sides of a, b, and c where c is the hypotenuse, or side opposite the right angle.

The formula he derived was known as the pythagorean theorem:

a^2+b^2=c^2 (The ^2 means an exponent of 2, or squared).

This is read as a squared + b squared = c squared.

For example, if there was a right triangle with the sides of 3, 4, and 5, then a would be 3b would be 4, and c would be 5.

Plug this into the formula, and it works!

3^2+4^2=5^2. Simplifying the squares, we get:

9+16=25. Simplifying by addition, we get the true statement:


The pythagorean theorem can be applied in numerous ways, and here I'll give an example. Let's say you have a TV and you need to find the length of the diagonal going across. You know that the sides are exactly 3 feet by 5 feet. It doesn't matter which you make a or b, so let's make:

a=3b=5. We want to find c, the unknown variable, the diagonal. Plug this into the equation and get:

3^2+5^2=c^2. Simplify the squares and get:

9+25=c^2. Simplify this using addition and get:

34=c^2. Now, we need to solve for c. C squared equals 34, so we need to take the square root of 34. Using a calculator, we can approximate:


So, using the Pythagorean theorem, we found that the hypotenuse was about 5.8 feet!

Hope this helped, thanks!

Here's a good visualization of the Pythagorean Theorem:


flag Report DMCA

Excellent job

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors