Pythagoras Theorem

Q. In a rectangle with sides 6 cm and 8 cm, what is the length of the diagonal?

1. 16 cm
2. 14 cm
3. 12 cm
4. 10 cm

Q. In a right angle triangle ABC right angled at B, if AB = 5 cm, AC = 13 cm, then BC is

1. 10 cm
2. 12 cm
3. 15 cm
4. 6 cm

Q. Foot of a 10m long ladder leaning against a vertical wall is 6m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.

Q. If the side of the square is $7\text{cm}$, what will be the length of its diagonal?

1. $7\sqrt{2}\text{cm}$
2. $2\sqrt{7}\text{cm}$
3. $14\text{cm}$
4. $7\sqrt{2}\text{cm}$

Q.

If the distance between the top of two trees of height 20 m and 28 m is 17 m, then the horizontal distance between the trees is:

1. 11 m

2. 31 m

3. 15 m

4. 9 m

Q.

Question 62

The area of a rectangular field is $48m^2$ and one of its sides is 6m. How long will a lady take to cross the field diagonally at the rate of 20 m/min?

Q.
Two poles, of height 7m and 12m are 12 metres apart.
If the top of the two poles are to be connected with a wire, find the length of the wire required.

1. 11 m
2. 12 m
3. 13 m
4. 14 m

Q.

Are the diagonals of a rectangle equal? Why?

Q. To which of these triangles is the Pythagoras Theorem applicable?

1. A scalene triangle
2. An acute-angled triangle
3. A right-angled triangle
4. An obtuse-angled triangle

Q. Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangle drawn on the other two sides of the triangle.

Q. Which of the following can be the sides of a right-angled triangle?

1. $1,1,\sqrt{3}$
2. 3, 3, 3
3. 3, 4, 5
4. 4, 5, 6

Q.

In the figure, AC=10cm, PC= 15cm, PQ=12cm, find PB?

1. 8cm

2. 9cm

3. 6cm

4. 7cm

Q. Ankit walks 4m from his house towards west. He then turns towards south and walks for 5m to reach a temple. Find the shortest distance between his house and the temple.

1. $\sqrt{65}$ m
2. 7 m
3. 8 m
4. $\sqrt{41}$ m

Q. In the given figure, ABCD is a rhombus. Find the values of x, y and z.

1. x = 13
   y = 6
   z = 2.5
2. x = 13
   y = 12
   z = 5
3. x = 12
   y = 5
   z = 13
4. x = 13
   y = 24
   z = 10

Q. A fireman places a 20 m long ladder against the wall of a building to enter a window at a height of 12 m from the ground, what is the distance between the base of the ladder and the building?

1. 18 m
2. 22 m
3. 12 m
4. 16 m

Q. Which of the following have all sides equal?

1. Parallelogram
2. Trapezium
3. Rectangle
4. Square

Q.

State whether the given statement is true or false:

3, 4, 5 is a Pythagorean triplet.

1. True

2. False

Q. What is a Hypotenuse?

Q.

In a right triangle ABC, ∠B = 90°.

(a) If AB = 6 cm, BC = 8 cm, find AC

(b) If AC = 13 cm, BC = 5 cm, find AB

Q.

In a right-angled triangle, the length of the longest side is 10 cm and of another side is 8 cm. What will be the length of the third side?

1. 6 cm
2. 7 cm
3. 9 cm
4. 5 cm

Q. The perimeter of a rhombus is equal to the perimeter of square. If length of diagonal of square is $20\sqrt{2}$ cm and one of the diagonals of rhombus is 32 cm then area of rhombus is

1. $480{\text{cm}}^2$
2. $384{\text{cm}}^2$
3. $360{\text{cm}}^2$
4. $420{\text{cm}}^2$

Q. The ratio of the sides AB : BC : AC is equal to

1. 5 : 13 : 12
   
2. 12 : 13 : 5
   
3. 5 : 12 : 13
   
4. 13 : 5 : 12

Q.

In a ΔABC, AB = BC and ∠B = 64°. Find ∠C.

Q.

In the given figure, AB equal to ___ units.

1. $3\sqrt{2}$

2. $2\sqrt{2}$

3. $4\sqrt{2}$

4. $\sqrt{2}$

Q. A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4m high. If the foot of the ladder is moved 6m towards the wall then find the distance by which the top of the ladder would slide upwards on the wall.

Q. The perimeter of the rhombus is 32 cm. Then What is the length of its side?

Q.

A right-angle triangle has a hypotenuse of length $Q\mathrm{cm}$ and one side of length $P\mathrm{cm}$. If $Q-P=2$ express the length of the third side of the right-angle triangle in terms of $Q$.

Q. Question 74
Fill in the blanks to make the statements true.​​​​​​​
In a rhombus, diagonals intersect at ___ angles.

Q. In a rectangle, length of two sides are given as 20 and 21 cm. Find the length of the diagonal in cm.

1. 29

Q.

Question 14

Write the correct answer from the given four options.

The hypotenuse of a right-angled triangle with its legs of lengths $3x\times 4x$ is

a) 5x
b) 7x
c) 16x
d) 25x