# Pythagoras Theorem

## Trending Questions

**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 34 m and 29 m respectively. If the distance between the two buildings is 12m, find the distance between the top of the buildings.

12 m

13 m

16 m

14 m

**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 =

10

13

25

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 5 m from the ground and its top touches the ground at a distance of 12 m 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 √50.

- True
- 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.

7 m

17 m

24 m

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.

- True
- 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.

- 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.

- 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

- Acute triangle
- Right triangle
- Obtuse triangle

**Q.**

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

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

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

Both P and Q are true

P is true and Q is false

P is false and Q is true

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