# 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

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