On this page you can read Pythagoras Premay because Pythagoras theorem is used while solving maths problems.

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## what is pythagoras theorem

If any triangle obeys the Pythagorean theorem, then it is definitely a right angled triangle.

The Pythagorean theorem establishes the relationship between the sides of a triangle. The Pythagorean theorem was originated by Pythagoras.

Pythagoras was a 6th century BC Greek philosopher who declared an essential property of right triangles. Hence the name “Pythagoras Theorem” was named after Pythagoras.

## prove pythagoras theorem

**Statement :-** In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

**Given :-** In ABC B = 90°

**composition :-** BD AC

**To prove :- **AC² = AB² + BC

**Origin :-**

In ADB and ABC

ADB = ABC = 90°

A = A (Common)

ADB ~ ABC

So AD/AB = AB/AC

AD × AC = AB² ………..(1)

In BDC and ABC

BDC = ABC = 90°

C = C (Common)

BDC ~ ABC

So DC/BC = BC/AC

DC × AC = BC² ………..(2)

Adding equation (1) and equation (2),

AD × AC + DC × AC = AB² + BC²

AC(AD + DC) = AB² + BC²

AD + DC = AC

AC × AC = AB² + BC²

AC² = AB² + BC

This was to be proved.

## Pythagoras Theorem Question Answer

Question 1. In a right angled triangle, the side of the perpendicular is 3 cm, the side of the base is 4 cm, then what will be the side of the hypotenuse of Pythagoras?

A. 2 cm

B. 5 cm

C. 7 cm

D. 9 cm

Solution:- According to the question,

From the Pythagorean theorem,

(hypotenuse)² = (perpendicular)² + (base)²

AC² = AB² + BC

AC² = (3)² + (4)²

AC² = 9 + 16

AC² = 25

AC = 25

AC = 5

Hence the side of the hypotenuse will be 5.

Answer:- 5 cm

Question 2. Angle B of triangle ABC is right angled. If AB = 5 cm and BC = 12 cm, then find the length of AC?

A. 3 cm

B. 10 cm

C. 13 cm

D. 16 cm

Solution:- According to the question,

From the Pythagorean theorem,

AC² = AB² + BC

AC² = (5)² + (12)²

AC² = 25 + 144

AC² = 169

AC = 169

AC = 13

Hence, the length of AC will be 13 cm.

Answer:- 13 cm

Question 3. A ladder is placed against a wall in such a way that its base is at a distance of 4 m from the wall and its top rests on a window at a height of 5 m from the ground. Find the length of the ladder.

A. 1 meter

B. 2 meters

C. 3 meters

D. 4 meters

Let AB be a ladder and BC be the wall with window C.

BC = 4 m. and AC = 5 m.

From the Pythagorean theorem,

AC² = AB² + BC

AB² = AC² – BC²

AB² = (5)² – (4)²

AB² = 25 – 16

AB² = 9

AB = 9

AB = 3

Thus, the length of the ladder is 3 m.

Answer:- 3 meters

Question 4. Angle B of triangle ABC is right angled. If AC = 15 cm and BC = 12 cm, then find the length of AB?

A. 3 cm

B. 6 cm

C. 9 cm

D. 12 cm

Solution:- According to the question,

The triangle is a right angled triangle, hence the Pythagorean theorem,

AC² = AB² + BC

AB² = AC² – BC²

AB² = (15)² – (12)²

AB² = 225 – 144

AB² = 81

AB = 81

AB = 9

Hence, the length of AB will be 9 cm.

Answer:- 9 cm

Question 5. Angle B of triangle ABC is right angled. If AC = 34 cm and AB = 30 cm, then find the length of BC?

A. 8 cm

B. 16 cm

C. 9 cm

D. 32 cm

Solution:- According to the question,

AC = 34

AB = 30

BC = ?

The triangle is a right angled triangle, hence the Pythagorean theorem,

AC² = AB² + BC

BC = AC² – AB²

BC² = (34)² – (30)²

BC² = 1156 – 900

BC² = 256

BC = 256

BC = 16

Hence, the length of BC will be 16 cm.

Answer:- 16 cm

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