IXL | Pythagorean theorem: word problems

There is a rope running from the top of a flagpole to a hook in the ground. The flagpole is 15 meters high, and the hook is 8 meters from its base. How long is the rope?

meters

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Learn with an example

question

Troy measured the floor of his storage unit, which is rectangular. It is 4 feet wide and 5 feet from one corner to the opposite corner. How long is the storage unit?

feet

key idea

In a right triangle, a² + b² = c², where a and b are the lengths of the legs and c is the length of the hypotenuse. This is called the Pythagorean theorem.

solution

Draw a diagram.

4 ft

5 ft

Use the Pythagorean theorem, with b = 4 and c = 5.

Pythagorean theorem

a² + b²

c²

Pythagorean theorem

Plug in b = 4 and c = 5

a² + 4²

5²

Plug in b = 4 and c = 5

Square

a² + 16

Square

Subtract 16 from both sides

a²

Subtract 16 from both sides

Take the square root of both sides

a²

Take the square root of both sides

Simplify

The storage unit is 3 feet long.

Looking for more? Try these:

Lesson: The Pythagorean theorem

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Teacher tools

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T.3Pythagorean theorem: find the missing leg or hypotenuse length

Lesson: The Pythagorean theorem

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