Application of Pythagoras Theorem

Q.

The square of the hypothenuse of a right-angled isosceles triangle is $128$m. Find the length of the sides.

Q.

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

1. 13

2. 26

3. 30

4. 25

Q.

A ship sails 14 nautical km due East and 48 nautical km due North. How far is it from the starting point ?

1. 45 nautical km

2. 50 nautical km

3. 25 nautical km

4. 13 nautical km

Q. $△$ABC is right angled at A. If BC = 60 cm and AC = 61 cm, then find the length of the side AB.

Q.

If a right angle triangle has sides of lengths 'a' and 'b' and hypotenuse of length 'c', then

1. $c^2-a^2=b^2$

2. $a^2-c^2=b^2$

3. $b^2-a^2=c^2$

4. $c^2-b^2=a^2$

Q. A man goes to a garden and runs in the following manner: From the starting point, he goes west $25m$ then due north $60m$, then due east $80m$ and finally due south $12m.$ The distance between the finishing point and the starting point is:

1. $177m$
2. $103m$
3. $83m$
4. $73m$

Q. It is easy to construct sets of Pythagorean Triples, When m and n are any two ............... integers.

1. Alternative
2. Equal
3. Negative
4. Positive

Q.

The hypotenuse of a right angled triangle is 25 cm. The other two sides are such that one is 5 cm longer than the other. Their lengths (in cm) are

1. $10,15$

2. $20,25$

3. $25,30$

4. $15,20$

Q.

$ABC$ is a triangle, right-angled at $C$. If $\overline{AB}$ $=25cm$ and $\overline{AC}$ $=7cm$ find $\overline{BC}$.

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. 10

2. 16

3. 14

4. 13

Q.

A ship sails 30 nautical km due West and 16 nautical km due North. How far is it from its starting point ?

1. 20 nautical km

2. 17 nautical km

3. 13 nautical km

4. 34 nautical km

Q.

In a $△ABC$ right angled at B , the length AC is 37 cm and AB = 12 cm. Find the length of BC

1. SSS

2. ASA

3. RHS

4. SAS

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.

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

1. 10

2. 15

3. 25

4. 20

Q.

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

1. 51

2. 11

3. 12

4. 21