IXL - Pythagorean theorem: word problems (Algebra 1 practice)

An envelope measures 9 centimeters by 12 centimeters. A pencil is placed in the envelope at a diagonal. What is the maximum possible length of the pencil?

centimeters

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Learn with an example

question

Three baseball players are playing catch. Sally is 3 meters south of Darnell and 4 meters west of Julia. How far does Darnell need to throw the ball to get it to Julia?

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.

3 m

4 m

Use the Pythagorean theorem, with a = 3 and b = 4.

Pythagorean theorem

a² + b²

c²

Pythagorean theorem

Plug in a = 3 and b = 4

3² + 4²

c²

Plug in a = 3 and b = 4

Square

9 + 16

c²

Square

Add

c²

Add

Take the square root of both sides

c²

Take the square root of both sides

Simplify

Darnell needs to throw the ball 5 meters.

Looking for more? Try these:

Lesson: The Pythagorean theorem

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Lesson: The Pythagorean theorem

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