We want to write a problem that can be solved using the Pythagorean Theorem. Then we should explain how to solve it. Here is the problem.
Imagine we are buying a TV. The width of the TV is 52.3 inches, and its height is 42 inches. We are asked to find the screen size of the TV, which is the length of its diagonal.
We can model this situation in the graph.
Notice that a right triangle formed. The lengths of its legs are 52.3 and 42 inches. We want to find the third length — the length of the hypotenuse. Let c be that missing length.
Remember the Pythagorean Theorem. This theorem tells us about the relationship between the legs a and b and the hypotenuse c.
Pythagorean Theorem
In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
We can also write this theorem using the given lengths.
There are two approximate solutions to the equation, c=- 67 and c=67. Because a length cannot be negative, c=67 is our solution. As a result, the size of the TV screen is 67 inches, or 67".
