Pythagoras Theorem

Q.

What is $a$ square plus $b$ square?

Q.

Write a Pythagorean triplet whose smallest number is $8$ and verify your answer.

Q.

5, 12, 13 is a Pythagorean triplet.

1. True

2. False

Q.

The tops of two poles of height 20m and 14m are connected by a wire. If the wire makes an angle of 30 degree with horizontal, then the length of the wire is:

1. 6m

2. 10m

3. 8m

4. 12m

Q.

8, 15, 17 is a Pythagorean triplet

1. False

2. True

Q.

$3,4,5$ is a Pythagorean triplet.

1. False

2. True

Q.

7, 24, 25 is a Pythagorean triplet.

1. True

2. False

Q. Diagonals PR and QS of a rhombus PQRS are 20 cm and 48 cm respectively. Find the length of side PQ.

Q.

Write a pythagorean triplet whose one member is $14$.

Q.

Each of the two equal sides of an isosceles right triangle is $10cm$ long. Its area is.

1. $10\sqrt{3}c{m}^2$

2. $50c{m}^2$

3. $5\sqrt{10}c{m}^2$

4. $75c{m}^2$

Q.

What is the area of a right angled triangle if its sides are 6cm, 8cm and 10cm?

1. 26cm²

2. 24cm²

3. 36cm²

4. 40cm²

Q.

Find a pythagorean triplet whose one number is $15$.

Q. Question 5
A field is in the shape of trapezium having parallel sides 90m and 30m. These sides meet the third side at right angles. The length of the fourth side is 100m. If it costs Rs.4 to plough $1m^2$ of the field, find the total cost of ploughing the field.

Q.

In a right triangle, the hypotenuse is $6m$ more than twice the shortest side. If the third side is $2m$ less than the hypotenuse. Then the length of the hypotenuse is

1. 22

2. 24

3. 28

4. 26

Q.

$\frac{1}{2}\times \text{base}\times \text{height}$ is the formula for which type of triangles?

1. Right angled triangles

2. Isosceles triangles

3. Equilateral triangles

4. Scalene triangles

Q.

The area of an equilateral triangle having a side length equal to $\frac{\sqrt{3}}{4}cm$ is

1. $\frac{2}{27}{cm}^2$

2. $\frac{2}{15}{cm}^2$

3. $\frac{3\sqrt{3}}{64}{cm}^2$

4. $\frac{3}{14}{cm}^2$

Q.

In a trapezium ABCD, if AB || CD then $(A{C}^2+B{D}^2)$ = ?

(a) $B{C}^2+A{D}^2+2BC.AD$

(b) $A{B}^2+C{D}^2+2AB.CD$

(c) $A{B}^2+C{D}^2+2AD.BC$

(d) $B{C}^2+A{D}^2+2AB.CD$

Q. If the perimeter of an equilateral triangle is 60 cm, then its area is 1732 $c{m}^2$.

1. False
2. True

Q.

Can a right triangle with sides $6\mathrm{cm}$, $10\mathrm{cm}$ and $8\mathrm{cm}$ be formed? Give reason.

Q.

In $∆ABC,$ if $(a+b+c)(a-b+c)=3ac,$ then

1. $\angle B=60°$

2. $\angle B=30°$

3. $\angle C=60°$

4. $\angle A+\angle C=90°$

Q. Which of the following are not the sides of a right angled triangle?
A. 5, 12, 13
B. 6, 8, 10
C. 10, 24, 25
D. 7, 24, 25

1. $A$
2. $B$
3. $D$
4. $C$

Q.

If $a,b,c$ are in G.P ., then $a(b^2+c^2)$ is

Q. The area of an isosceles triangle whose base = 10 cm and equal sides = 13 cm is (in $c{m}^2$).

1. 60
2. 30
3. 12

Q. Dear Sir,
Please help me with the question below.

What is the conclusion for a square root spiral ?

Q.

Let $y=y\left(x\right)$ be the solution of the differential equation $xdy–ydx=\sqrt{x^2-y^2}dx,x\ge 1,withy\left(1\right)=0$. If the area bounded by the line $x=1,x=e^{\mathrm{\pi }},y=0andy=y\left(x\right)is\alpha e^{2\mathrm{\pi }}+\beta ,$ then the value of $10(\alpha +\beta )$ is equal to:

Q. Which of the following are not the sides of a right angled triangle?

1. 5, 12, 13
2. 6, 8, 10
3. 10, 24, 25
4. 7, 24, 25

Q.

The Pythagoras theorem states that, in a right-angled triangle, the square of its hypotenuse is equal to the sum of its other two sides.

1. True

2. False

Q. If the sides of a right-angled triangle are 20 cm and 21 cm. Find the hypotenuse.

1. 26 cm
2. 27 cm
3. 28 cm
4. 29 cm

Q. Question 9 (i)
In triangle ABC, right-angled at B, if $tanA=\frac{1}{\sqrt{3}}$, find the value of:
(i) sinAcosC + cosAsinC

Q.

A ladder is placed against a wall such that its foot is at a distance of $3m$ from the wall and its top reaches $4m$ above the ground. Find the length of the ladder.

1. $6m$

2. $5m$

3. $25m$

4. $10m$