# Questions and answers related to what is Pythagoras theorem

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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 :-
A = A (Common)
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
AC × AC = AB² + BC²
AC² = AB² + BC
This was to be proved.

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.

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.

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.

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.

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.