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.

c² = a² + b²

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.

Hypotenuse² = 11² + 13² = 121 + 169 = 290

So, length of hypotenuse = $\sqrt{290}$ = 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

8² = 6² + x²

64 = 36 + x²

x² = 64 – 36 = 28

x = $\sqrt{28}$ = 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.

ques_traiangle

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?

rectang

Answer key

6.3 units
15 cm
9.5 units
13 feet
17 cm

Personalized Online Tutoring

eTutorWorld offers affordable one-on-one live tutoring over the web for Grades 2-12, Test Prep help for Standardized tests like SCAT, CogAT, SSAT, SAT, ACT, ISEE and AP. You may schedule online tutoring lessons at your personal scheduled times, all with a Money-Back Guarantee. The first one-on-one online tutoring lesson is always FREE, no purchase obligation, no credit card required.

For answers/solutions to any question or to learn concepts, take a FREE Demo Session.

Schedule a Free Session

No credit card required, no obligation to purchase.
Just schedule a FREE Sessions to meet a tutor and get help on any topic you want!

Pricing for Online Tutoring

Tutoring Package	Validity	Grade (1-12), College
5 sessions	1 Month	$139
1 session	1 Month	$28
10 sessions	3 months	$269
15 sessions	3 months	$399
20 sessions	4 months	$499
50 sessions	6 months	$1189
100 sessions	12 months	$2249