# Pythagorean Theorem

Home | Online Math Tutoring | 8th Grade Math Tutoring | **Pythagorean Theorem**

The Pythagoras’ Theorem states that if a triangle has right angle, and squares are made on each of the three sides, then the biggest square has exactly the same area as the other two squares put together.

c^{2} = a^{2} + b^{2}

Here *c* is the longest side of the triangle, which is called the hypotenuse and it is always opposite to the right angle.

Pythagoras’ Theorem state that square of the hypotenuse is equal to the sum of square of the other two sides.

*Example:* Find the hypotenuse of the given right-angled triangle. Give your answer to the nearest tenth.

Hypotenuse^{2} = 11^{2} + 13^{2} = 121 + 169 = 290

So, length of hypotenuse = = 17.02 ≅ 17** **cm (to the nearest tenth)

*Example:* If the hypotenuse of a right angled triangle is 8 units and one of the sides is 6 units, then what is the length of the third side?

Let us assume the third side = *x* cm

8^{2} = 6^{2} + *x*^{2}

64 = 36 + *x*^{2}

*x*^{2} = 64 – 36 = 28

*x* = = 5.29 ≅ 5.3 cm (to the nearest tenth)

**CHECK POINT**

1.What is length of the diagonal of rectangle with length 6 units and width 2 units? (Round your answer to the nearest tenth)

2.Find the length of hypotenuse of the given triangle.

3.If the hypotenuse of a right-angled triangle is 10 units and one of the sides is 3 units, then what is the length of the third side? (Round your answer to the nearest tenth)

4.If Daniel placed a ladder 4 feet from the wall and top of the ladder rests 10 feet up on the wall, then what is the length of the ladder?

5.Angel wants to cut a rectangular sheet measuring 8 cm by 15 cm for her crafts class. What is the diagonal length of the sheet?

##### Answer key

- 6.3 units
- 15 cm
- 9.5 units
- 13 feet
- 17 cm

Home

Summer Courses 2020

Tutoring

Test Prep

Worksheets

Pricing

About Us

Blog

Free Trial

Login

Terms of service

Privacy Policy

Money Back Guarantee

Technical requirements

FAQs

Job Opportunities

Sitemap

**Connect with us**

+1-269-763-4602

+1-269-763-5024

**Online test prep and practice**

SCAT

CogAT

SSAT

ISEE

PSAT

SAT

ACT

AP Exam

**Science Tutoring**

Physics Tutoring

Chemistry Tutoring

Biology Tutoring

**Math Tutoring**

Pre-Algebra Tutoring

Algebra Tutoring

Pre Calculus Tutoring

Calculus Tutoring

Geometry Tutoring

Trigonometry Tutoring

Statistics Tutoring

©2020 eTutorWorld Terms of use Privacy Policy Site by Little Red Bird

©2020 eTutorWorld

Terms of use

Privacy Policy

Site by Little Red Bird