Pythagorean theorem word problems
Pythagorean-theorem-word-problems 256
Exercise Name: Pythagorean theorem word problems
Math Missions: 8th grade (U.S.) Math Mission, High school geometry Math Mission
Types of Problems: 6

The Pythagorean theorem word problems exercise appears under the 8th grade (U.S.) Math Mission and High school geometry Math Mission. This exercise has several applications of the Pythagorean Theorem.

Types of Problems

There are six types of problems in this exercise:

  1. Find the area of the triangle: This problem asks the use to use the Pythagorean Theorem to find a third side of a right triangle for calculating the triangle's area.

    Find the area of the triangle

  2. Find the specified length: This problem has many right triangles that may need to be used together to find a specific length.

    Find the specified length

  3. Solve the problem to determine straightness: This problem provides a word problem that involves an object that may or may not be crooked. The user can use the Pythagorean Theorem to determine if a certain object is "staright."

    Solve the problem to determine straightness

  4. Find the distance described: This problem involves a situation with a person moving in compass directions. Users are expected to find the straight-line distance from the beginning of the trip to the end.

    Find the distance described

  5. Apply the Pythagorean theorem and rates: This problem uses the Pythagorean Theorem to find a distance and then use a given rate to determine how long it takes people to complete a trip.

    Apply the Pythagorean theorem and rates

  6. Determine the Pythagorean triples: This problem provides sets of three numbers and the user is asked to determine all such sets that make a Pythagorean triple.

    Determine the Pythagorean triples


The Pythagorean Theorem is one of the most famous theorem in all of mathematics. This exercise requires knowledge of that theorem and of the fact that distance equals rate times time.

  1. The Pythagorean Theorem says that in a right triangle the sum of the squares of the legs is equal to the square of the hypotenuse. In symbols,  {a^2+b^2=c^2} where {c} is the label on the hypotenuse.
  2. The amount of time it takes to travel a distance is distance/rate.

Real-life applications

  1. The Pythagorean Theorem was famously used in ancient Egypt for creating monuments and ensuring measuring objects.
  2. The Pythagorean Theorem is vital to the development of trigonometry and the applications of trigonometry are practically countless.
  3. The word problems in this exercise are applications of the theorem also.
  4. Geometric concepts, such as the ones used in this exercise, are instrumental in architecture (drafting), art and graphical design.

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