In these worksheets, students will learn to solve word problems using the Pythagorean theorem.

The Pythagorean Theorem is the expression of the relationship between the three sides of a right triangle (the square of the hypotenuse is equal to the sum of the squares of the other two sides). In these worksheets, your students will solve word problems that require them to use the Pythagorean Theorem. There are 11 worksheets in this set. A set of six worksheets introduces the topic and provides problems for students to practice. Additional worksheets are provided at both the basic and intermediate skills levels. This set of worksheets contains lessons, step-by-step solutions to sample problems, and both simple and more complex problems. It also includes ample worksheets for students to practice independently. Students may require extra paper on which to do their calculations. Most worksheets contain between eight and ten problems. When finished with this set of worksheets, students will be able to solve word problems that require them to use the Pythagorean Theorem.

It should be noted that right triangles can also be used to model physical elevations or depressions of just about any kind. There is a set process you should follow when you come across a challenging word problem that involves the use of the Pythagorean Theorem. It starts by drawing a right triangle and adding all the information you have on the measures of the triangle. Then we can use the Pythagorean Theorem (a2 + b2 = c2) to find any of the missing sides. The measures a and b represent the legs of the triangle and c represents the hypotenuse (which is opposite the right angle). Place the known values of the triangle in the equation and solve the equation to find the missing side. The last thing to keep in mind is the units of measure. Make certain those units are consistent. These worksheets explain how to solve word problems using the Pythagorean Theorem. Sample problems are solved and practice problems are provided.

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Pythagorean Theorem Word Problems Worksheets

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Topic Lesson

What is the width of rectangle whose diagonal is 13 cm and length is 12 cm?

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Skill Lesson and Practice

John leaves school to go home. He walks 6 blocks North and then 8 blocks west. Find shortest distance between John's home and the school?

Practice Worksheet

Bob takes a shortcut along the diagonal of a rectangular plot that is 32cm wide and 24 cm long, instead of going along the sides. How much does that shorten his path?

Pythagorean Theorem Word Problems Practice

4 An airplane is flying at the altitude of 650 m, and is at the distance of 3.5 km from the airport. What is the airplaneā€™s ground distance from the airport?

Group Pack Drills

A 17 feet ladder is placed on the wall of a house so that its lower end is 11 feet from the wall. At what height does the ladder touch the house?

Topic Warm Up

House A is 9 miles from house B, and 40 miles from house C. House A, B and C are forming a right triangle at A. A road connects houses B and C directly. Find the length of this road.

Pythagorean Theorem Word Problems Basic Skills Worksheet

A baseball diamond is a square with sides of 80 feet. What is the shortest distance, to the nearest tenth of a foot, between first base and third base?

Basic Skills Practice Worksheet 2

Slanted sides of a tent 11 feet long total and the bottom of the house is 120 feet across. What is the tallest point of this tent?

Intermediate Skills Worksheet

In South, settlers often fashioned tents as an isosceles triangle. How long would the cloth have to be so that the opening of the tent was 5 meters high and 24 meters wide?

Topic Skills Check

Betty drives her car 160 km south and then 36 km east. How far is she from her starting point?

Intermediate Skills Drill

Firefighters have a 117 feet extension ladder. In order to reach 108 feet up a building, how far away from the building should the feet of the ladder be placed?