IXL | Pythagorean theorem: word problems

Kingwood Street and Newberry Avenue intersect. If the diagonal distance across the intersection is 17 meters and Kingwood Street is 15 meters wide, how wide is Newberry Avenue?

meters

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Learn with an example

question

A pigeon was sitting 8 meters from the base of a telephone pole and flew 17 meters to reach the top of the pole. How tall is the telephone pole?

meters

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.

8 m

17 m

Use the Pythagorean theorem, with b = 8 and c = 17.

Pythagorean theorem

a² + b²

c²

Pythagorean theorem

Plug in b = 8 and c = 17

a² + 8²

17²

Plug in b = 8 and c = 17

Square

a² + 64

289

Square

Subtract 64 from both sides

a²

225

Subtract 64 from both sides

Take the square root of both sides

a²

225

Take the square root of both sides

Simplify

The telephone pole is 15 meters tall.

Looking for more? Try these:

Lesson: The Pythagorean theorem

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Teacher tools

Work it out

Not feeling ready yet? These can help:

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

Lesson: The Pythagorean theorem

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