Pythagorean Triplets

Q. Find the Pythagorean triplets from among the following sets of numbers.
(i) 3, 4, 5
(ii) 2, 4, 5
(iii) 4, 5, 6
(iv) 2, 6, 7
(v) 9, 40, 41
(vi) 4, 7, 8

Q. The sides of a triangle are of length 8 cm, 15 cm and 17 cm. Then this triangle is a right triangle.

1. True
2. False

Q.

In a right angled triangle , the measure of the hypotenuse is 41 cm and measure of one of the side is 9 cm, find the measure of the third side

1. 40 cm

2. 20 cm

3. 21 cm

4. 24 cm

Q.

What are applications of Pythagorean theorem in daily life.

Q.

Pythagorean triplets are a set of three numbers in which the following relation holds true:

The sum of the squares of any two numbers is equal to the square of the third number.

1. False

2. True

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.

$△$ABC is right angled at A. If AB = 12 cm and AC = 16 cm, then BC = ____________ cm.

1. 10

2. 15

3. 20

4. 25

Q.

A right triangle has a hypotenuse of length $pcm$ and one side of length $qcm$. If $p-q=1$, find the length of the third side of the triangle :

Q.

$△$ABC is right angled at A. If BC = 60 cm and AC = 61 cm, then AB = ____________ cm.

1. 11

2. 12

3. 21

4. 51

Q.

A guy wire attached to a vertical pole of height $18m$ is $24m$ long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?

Q.

In the adjoining figure , $\angle BAC=90°$

BC = 130 , AC = 50 , find the length of AB

1. 12 m

2. 102 m

3. 150 m

4. 120 m

Q. Find the hypotenuse of right angled triangle if the other sides are $3,4$ respectively.

1. 5
2. 3
3. 2
4. 1

Q. A Pythagorean triplet whose smallest member is $8$, is:

1. $8,15,18$
   
2. $8,14,17$
3. $8,13,16$
4. $8,15,17$
   

Q. is (5, 12, 13) a pythagorean triple?

Q. Write the length of the hypotenuse of the following right angled $△ABC$.

Q. Check if the lengths 18 cm, 24 cm, and 30 cm be the sides of a right-angled triangle?

Q. In a right angled triangle the square of the hypotenuse is twice the product of the square of the other sides. Then the triangle is

1. equilateral
2. isosceles
3. of $\angle s{30}^o,{60}^o,{90}^o$
4. of $\angle s{40}^o,{50}^o,{90}^o$

Q. Consider a right triangle with legs of length $a$ and $b$ and hypotenuse of length $c$. Of $k$ denotes the area of the triangle then the value of $(a+b)$ equals

1. $\sqrt{c^2+4k}$
2. $\frac{c^2}{4\sqrt{k}}$
3. $\frac{4k}{c}$
4. $c+2\sqrt{k}$

Q. If the sides of a right angled triangle are $x,3x+3$ and $3x+4$, then $x$ is equal to:

1. $7$
2. $6$
3. $-1$
4. Both A and B