Pythagoras Theorem

Q.

How is the Pythagorean theorem used in real life?

Q.

Why does the Pythagorean theorem only work for right triangles?

Q.

The heights of the two buildings are $34m$ and $29m$ respectively. If the distance between the two buildings is 12m, find the distance between the top of the buildings.

1. $12m$

2. $13m$

3. $16m$

4. $14m$

Q. The top of a ladder of length 15 m reaches a window 9 m above the ground. What is the distance between the base of the wall and that of the ladder ?

Q.

$△$ABC is right angled at A. If AB = 10 cm and AC = 24 cm, then BC = _________ cm.

1. 10

2. 13

3. 25

4. 26

Q. Question 7
A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

Q.

A tree is broken at a height of $5m$ from the ground and its top touches the ground at a distance of $12m$ from the base of the tree. Find the original height of the tree.

Q.

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

Q. Question 1
PQR is a triangle, right angled at P. If PQ = 10 cm and PR = 24 cm, find QR.

Q. Verity that the numbers 12, 35, 37 represent Pythagorean triplet.

Q. In the right-angled ∆PQR, ∠ P = 90°. If l(PQ) = 24 cm and l(PR) = 10 cm, find the length of seg QR.

Q. In the right-angled ∆LMN, ∠ M = 90°. If l(LM) = 12 cm and l(LN) = 20 cm, find the length of seg MN.

Q. If the length of diagonal of a square is 10 cm, then the length of the side of the square is $\sqrt{50}$.

1. True
2. False

Q.

Two poles of heights 8 m and 15 m stand vertically on a plane ground. If the distance between their feet is 24 m, then find the distance between their top ends.

1. 7 m

2. 17 m

3. 24 m

4. 25 m

Q.

Question 8
The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.

Q.

The lengths 18 cm, 24 cm and 30 cm form the sides of a right-angled triangle.

1. True
2. False

Q. Angle opposite to angle LM in triangle LMN

Q.

Question 11

The top of a broken tree touches the ground at a distance of 12 m from its base. If the tree is broken at a height of 5 m from the ground, then the actual height of the tree is
a) 25 m
b) 13 m
c) 18 m
d) 17 m

Q.

Question 113

Jiya walks 6 km due east and then 8 km due north. How far is she from her starting place?

Q. Question 9
A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from the base of the wall.

Q.

Sachin walks $20$ km towards North. He turns left and walks $40$ km. He again turns left and walks $20$ km. Finally he moves $20$ km after turning to the left. How far is he from his starting position?

Q. A man goes 35 m due north and then 12 m due west. Find his distance (in m) from the starting point.

1. 37

Q.

Question 13

Two trees 7 m and 4 m high stand upright on a ground. If their bases (roots) are 4 m apart, then the distance between their tops is

a) 3 m
b) 5 m
c) 4 m
d) 11 m

Q.

Question 139

Height of a pole is 8 m. Find the length of rope tied with its top from a point on the ground at a distance of 6 m from its bottom.

Q. In a right angle triangle ABC right angled at B, if AB = 4 cm, BC = 3 cm, then AC = _____ cm.

1. 5

Q.

A man walks $5m$due south and then $12m$due east. Find his distance from the starting point.

Q.

Evaluate by using brackets $107\times 109$

Q. If the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a/an .

1. Acute triangle
2. Right triangle
3. Obtuse triangle

Q.

Let $f\left(x\right)={\left(1-x\right)}^2+{\sin }^{2}x+x^2$ for all $x\in \mathrm{ℝ}$ Consider the statements:

P: There exists some $x\in \mathrm{ℝ}$ such that $f\left(x\right)+2x=2\left(1+x^2\right)$

Q: There exists some $x\in \mathrm{ℝ}$ such that $2f\left(x\right)+1=2x\left(1+x\right)$. Then,

1. Both P and Q are true

2. P is true and Q is false

3. P is false and Q is true

4. Both P and Q are false

Q. A man goes 24m due east and then 10m due north . How far is he from his initial position