Video: Finding the Diagonal Length of a Rectangle Using the Pythagorean Theorem in a Real-World Context

A dining table is 24 ft long and 12 ft wide. Determine, to the nearest tenth, how far it is from one corner to the diagonally opposite corner.

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Video Transcript

A dining table is 24 feet long and 12 feet wide. Determine to the nearest tenth how far it is from one corner to the diagonally opposite corner.

So here we have a dining table. It’s 24 feet long and 12 feet wide. And we want to know how far it is from one corner to the diagonally opposite corner. And we can call this 𝑥. Something important to know would be that a table will have corners — 90-degree angles — and we can label that here. And we actually have a right triangle. So we can solve for 𝑥 using the Pythagorean theorem.

The Pythagorean theorem states the square of the longest side is equal to the sum of the squares of the shorter sides. The longest side is always across the 90-degree angle, called the hypotenuse. So this is will be our longest side and these will be our shorter sides. So let’s go ahead and plug them in.

𝑥 squared is equal to 24 squared plus 12 squared. And it doesn’t matter the order you put 24 or 12. You could put 12 squared plus 24 squared if we would like. 𝑥 squared is equal to 𝑥 squared and 24 squared is equal to 576 and 12 squared is equal to 144. Now, let’s add those numbers together and we get that 𝑥 squared is equal to 720.

So to solve for 𝑥, we need to square root both sides. And the square root of 720 is equal to 26.83. However, we need to round to the nearest 10th. So we need to decide whether to keep the eight an eight or round it up to a nine. Looking at the three, since it’s below five, we will keep the eight an eight. If it was five or above, we would round up to nine. This means the diagonally opposite corners are 26.8 feet far apart.

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