Pythagorean Triplets and Its Algebraic Patterns

Q. Which of the following are Pythagorean triplets?

1. (6, 8, 10)
2. (5, 12, 13)
3. (7, 13, 15)
4. (3, 4, 5)

Q.

If $24,x,26$ form a Pythagorean triplet with $26$ being the largest number, find $x$ ?

1. $8$

2. $9$

3. $10$

4. $11$

Q.

The sides of a right triangle whose hypotenuse is$17\mathrm{cm}$ are _________ and _________.

Q.

Find the area of a triangle whose sides are $12cm,35cm,37cm$.

1. $208c{m}^2$
2. $210c{m}^2$
3. $220c{m}^2$
4. $200c{m}^2$

Q. If the largest number in a Pythagorean triplet is 17, then what is the smallest number in that triplet?

1. 8
2. 9
3. 13
4. 12

Q.

Which of the following numbers can form sides of a right-angled triangle?

1. 10 cm , 6 cm , 8 cm

2. 2 cm , 17 cm , 9 cm

3. 4 cm , 5 cm , 9 cm

4. 13 cm , 27 cm , 15 cm

Q.

Which of the following cannot form a right-angled triangle, whose three sides are given below?

1. 7, 24, 25

2. 15, 20, 24

3. 24, 10, 26

4. 5, 12 , 13

Q.

A ladder of length 26m rests against a wall. If it reaches a height of 24 m from the ground, then the distance of the foot of the ladder from the wall is _________ m

1. 16

2. 14

3. 13

4. 10

Q.

Can a triangle with sides 8 cm, 15 cm and 16 cm form a right angle triangle?

1. False

2. True

Q. Which of the following is not a Pythogorean Triplet.
A. (5, 12, 13)
B. (7, 24, 25)
C. (9, 40, 41)
D. (9, 60, 61)

1. A
2. B
3. C
4. D

Q.

Which all of the following are pythagoras triplet

1. 5, 12, 13

2. 15, 8, 17

3. 9, 12, 16

4. 24, 10, 26

Q. Find the area of a right-angled triangle with hypotenuse of length 91 cm and height 35 cm.

1. $3472c{m}^2$
2. $3476c{m}^2$
3. $3848c{m}^2$
4. $3822c{m}^2$

Q. Out of the dates given below, which date constitutes a Pythagorean triplet?

1. 20/12/16

2. 13/08/15

3. 12/07/18

4. 16/10/25

Q.

In the given figure, AB = 15 cm, BC = 20 cm and CD = 7 cm. If $\angle ABC$ = $\angle ADC={90}^{\circ }$, then AD =____________cm

1. 25

2. 24

3. 15

4. 12

Q. The primitive Pythagorean triplet (3, 4, 5) is arguably the most famous and commonly used. Find the parameters m and n used in Euclid's formula to generate this triple.

1. 2, 2
2. 1, 1
3. 2, 1
4. 1, 3

Q. The lengths 18 cm, 24 cm and form the sides of a right-angled triangle.

1. 25 cm
2. 30 cm
3. 27 cm

Q.

In the given figure, if a = 9 cm and b = 12 cm, then c = ___

1. 20 cm

2. 12 cm

3. 10 cm

4. 15 cm

Q. The quantities 8a, 15a, 17a are pythagorian quantities.

1. True
2. False

Q.

In the given figure if AB = 20 cm DC = 10 cm and BC = 24 cm, then AD = _________ cm.

1. 13

2. 25

3. 30

4. 26

Q.

The quantities 8a, 15a, 17a from a Pythagorean triplet.

1. True

2. False

Q.

Which of the following is not a Pythagorean triplet?

1. 3, 4, 5

2. 10, 12, 13

3. 5, 12, 13

4. 7, 24, 25

Q.

In the given right angle triangle, if $Sin\theta =\frac{3}{5}$, then find the value of $3tan\alpha$.

1. 3

2. 5

3. 4

4. 1

Q. Which of the following is not a Pythagorean triplet?

1. 3, 4, 5
2. 7, 24, 25
3. 5, 12, 13
4. 8, 20, 25

Q.

Which of the following numbers can form sides of a right angled triangle?

1. 10 cm , 6 cm , 8 cm

2. 2 cm , 17 cm , 9 cm

3. 4 cm , 5 cm , 9 cm

4. 13 cm , 27 cm , 15 cm

Q.

Which of the following is right angled triangle having three side given below

1. 7, 24, 25

2. 15, 20, 24

3. 24, 10, 26

4. 5, 12 , 14

Q.

Which all of the following are Pythagorean triplets?

1. 5, 12, 13

2. 3, 4, 5

3. 9, 12, 16

4. 10, 24, 26

Q. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

Q.

6² - 1² = ___

1. 24²

2. 25²

3. 23²

4. 27²