Word problems on Pythagorean Theorem


Learn how to solve different types of word problems on Pythagorean Theorem.

Pythagoras Theorem can be used to solve the problems step-by-step when we know the length of two sides of a right angled triangle and we need to get the length of the third side.

Three cases of word problems on Pythagorean Theorem:

Case 1: To find the hypotenuse where perpendicular and base are given.

Case 2: To find the base where perpendicular and hypotenuse are given.

Case 3: To find the perpendicular where base and hypotenuse are given.


Word problems using the Pythagorean Theorem:

1. A person has to walk 100 m to go from position X in the north of east direction to the position B and then to the west of Y to reach finally at position Z. The position Z is situated at the north of X and at a distance of 60 m from X. Find the distance between X and Y.

Solution:

Let XY = x m

Therefore, YZ = (100 – x) m

In ∆ XYZ, ∠Z = 90°


Therefore, by Pythagoras theorem

XY2 = YZ2 + XZ2

⇒ x2 = (100 – x)2 + 602

x2 = 10000 – 200x + x2 + 3600
North South East West
Pythagorean Theorem Word Problem

200x = 10000 + 3600

200x = 13600

x = 13600/200

x = 68


Therefore, distance between X and Y = 68 meters.


2. If the square of the hypotenuse of an isosceles right triangle is 128 cm2, find the length of each side.

Solution:

Let the two equal side of right angled isosceles triangle, right angled at Q be k cm.

Word problems on Pythagorean Theorem
Given: h2 = 128

So, we get

PR2 = PQ2 + QR2

h2 = k2 + k2

⇒ 128 = 2k2

⇒ 128/2 = k2

⇒ 64 = k2

√64 = k

8 = k

Therefore, length of each side is 8 cm.


Using the formula solve more word problems on Pythagorean Theorem.

3. Find the perimeter of a rectangle whose length is 150 m and the diagonal is 170 m.

Word problem on Pythagorean Theorem

Solution:

In a rectangle, each angle measures 90°.

Therefore PSR is right angled at S

Using Pythagoras theorem, we get

⇒ PS2 + SR2 = PR2

⇒ PS2 + 1502 = 1702

⇒ PS2 = 1702 – 1502

⇒ PS2= (170 + 150) (170 – 150), [using the formula of a2 - b2 = (a + b) (a - b)]

⇒ PS2= 320 × 20

⇒ PS2 = 6400

PS = √6400

PS = 80

Therefore perimeter of the rectangle PQRS = 2 (length + width)

                                                          = 2 (150 + 80) m

                                                          = 2 (230) m

                                                          = 460 m


4. A ladder 13 m long is placed on the ground in such a way that it touches the top of a vertical wall 12 m high. Find the distance of the foot of the ladder from the bottom of the wall.

Word problems using the Pythagorean Theorem

Solution:

Let the required distance be x meters. Here, the ladder, the wall and the ground from a right-angled triangle. The ladder is the hypotenuse of that triangle.

According to Pythagorean Theorem,

x2 + 122 = 132

⇒ x2 = 132 – 122

⇒ x2 = (13 + 12) (13 – 12)

⇒ x2 = (25) (1)

⇒ x2 = 25

x = √25

x = 5

Therefore, distance of the foot of the ladder from the bottom of the wall = 5 meters.


5. The height of two building is 34 m and 29 m respectively. If the distance between the two building is 12 m, find the distance between their tops.

Pythagorean Theorem: Word Problems

Solution:

The vertical buildings AB and CD are 34 m and 29 m respectively.

Draw DE ┴ AB

Then AE = AB – EB but EB = BC

Therefore AE = 34 m - 29 m = 5 m

Now, AED is right angled triangle and right angled at E.

Therefor,

AD2 = AE2 + ED2

⇒ AD2 = 52 + 122

⇒ AD2 = 25 + 144

⇒ AD2 = 169

AD = √169

AD = 13

Therefore the distance between their tops = 13 m.

The examples will help us to solve various types of word problems on Pythagorean Theorem.

Congruent Shapes

Congruent Line-segments

Congruent Angles

Congruent Triangles

Conditions for the Congruence of Triangles

Side Side Side Congruence

Side Angle Side Congruence

Angle Side Angle Congruence

Angle Angle Side Congruence

Right Angle Hypotenuse Side congruence

Pythagorean Theorem

Proof of Pythagorean Theorem

Converse of Pythagorean Theorem






7th Grade Math Problems

8th Grade Math Practice

From Word problems on Pythagorean Theorem to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Roman Numerals | System of Numbers | Symbol of Roman Numerals |Numbers

    Feb 22, 24 04:21 PM

    List of Roman Numerals Chart
    How to read and write roman numerals? Hundreds of year ago, the Romans had a system of numbers which had only seven symbols. Each symbol had a different value and there was no symbol for 0. The symbol…

    Read More

  2. Worksheet on Roman Numerals |Roman Numerals|Symbols for Roman Numerals

    Feb 22, 24 04:15 PM

    Roman Numbers Table
    Practice the worksheet on roman numerals or numbers. This sheet will encourage the students to practice about the symbols for roman numerals and their values. Write the number for the following: (a) V…

    Read More

  3. Roman Symbols | What are Roman Numbers? | Roman Numeration System

    Feb 22, 24 02:30 PM

    Roman Numbers
    Do we know from where Roman symbols came? In Rome, people wanted to use their own symbols to express various numbers. These symbols, used by Romans, are known as Roman symbols, Romans used only seven…

    Read More

  4. Place Value | Place, Place Value and Face Value | Grouping the Digits

    Feb 19, 24 11:57 PM

    Place-value of a Digit
    The place value of a digit in a number is the value it holds to be at the place in the number. We know about the place value and face value of a digit and we will learn about it in details. We know th…

    Read More

  5. Math Questions Answers | Solved Math Questions and Answers | Free Math

    Feb 19, 24 11:14 PM

    Math Questions Answers
    In math questions answers each questions are solved with explanation. The questions are based from different topics. Care has been taken to solve the questions in such a way that students

    Read More

Congruent Shapes

Congruent Line-segments

Congruent Angles

Congruent Triangles

Conditions for the Congruence of Triangles

Side Side Side Congruence

Side Angle Side Congruence

Angle Side Angle Congruence

Angle Angle Side Congruence

Right Angle Hypotenuse Side congruence

Pythagorean Theorem

Proof of Pythagorean Theorem

Converse of Pythagorean Theorem