Visualisation of Pythagoras Theorem

Q.

A $5\text{m}$ long ladder is placed leaning towards a vertical wall such that it reaches the wall at the point $4\text{m}$ . If the foot of the ladder is moved $1.6\text{m}$ towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.

Q.

If the radius of a circle is 5 cm & length of a tangent PA from an external point P is 12 cm.Find the distance of point P from the centre of circle.

1. 9 cm

2. 18 cm

3. 13 cm

4. 7 cm

Q.

$PQR$ is a triangle right angled at $P$ and $M$ is a point on $QR$ such that $PM\perp QR$. Show that $\begin{array}{rcl}P{M}^2& =& QM\times MR\end{array}$.

Q.

$P$ and $Q$ are respectively the mid-points of sides $AB$ and $BC$ of a triangle $ABC$ and $R$ is the mid-point of $AP$, show that:

$ar\left(RQC\right)=\frac{3}{8}ar\left(ABC\right)$

Q. Find the value of AD in the given figure.


[3 Marks]

Q.

Refer to the following figure. Three squares are constructed on each side of the triangle as shown, with the length of each square equal to the side of the triangle on which it is constructed. The angle opposite to the blue colour square is the right angle. If the largest side is 17 cm, then find the sum of the areas of the three squares.

1. 289 $c{m}^2$

2. 578 $c{m}^2$

3. 143 $c{m}^2$

4. None

Q.

The diagram shows jib PQ of a crane.$PQ=20m$ . Find the height $QR$ when the reach $PR$ is $12m$

Q.

Refer to the following figure. Three squares are constructed on each side of the triangle as shown, with the length of each square equal to the side on which it is constructed. If the largest side is $13$, sum of the areas of the three squares is___. [The angle opposite to the blue colour square is the right angle]

Q.

A 13 m ladder is leaned against a wall as shown in figure. Find the distance of foot of ladder from the wall.

1. 1 m

2. 25 m

3. 2 m

4. 5 m

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. 31 m

2. 15 m

3. 9 m

4. 11 m

Q.

Refer to the following figure. Three squares are constructed on each side of the triangle as shown, with the length of each square equal to the side on which it is constructed. If the largest side is 13, sum of the areas of the three squares is___. [The angle opposite to the blue colour square is the right angle.]

Q.

Refer to the following figure. Three squares are constructed on each side of the triangle as shown, with the length of each square equal to the side of the triangle on which it is constructed. The angle opposite to the blue colour square is the right angle. If the largest side 5 cm, then find the sum of the area of the yellow square and brown square.

1. 25 $c{m}^2$

2. 9 $c{m}^2$

3. 13 $c{m}^2$

4. 4 $c{m}^2$

Q. In a magic square each row, column and diagonal have the same. Check which of the following is a magic square.

$1$	$-10$	$0$
$-4$	$-3$	$-2$
$-6$	$4$	$-7$

Q. Evaluate: $\frac{\sqrt{2}}{\sqrt[3]{32}}$

1. $2^{-\frac{1}{6}}$
2. $2^{-6}$
3. $2^{\frac{1}{6}}$
4. $2^6$

Q. The value of AD in the given figure is

1. 17 m
2. 19 m
3. 13 m
4. 18 m

Q.

Three squares are constructed on each side of the triangle as shown, with the length of each square equal to the side of the triangle on which it is constructed. The angle opposite to the blue colour square is the right angle. If the small two sides are 5 cm and 12 cm, then find the area of the blue square.

1. 289 $c{m}^2$

2. 225 $c{m}^2$

3. 64 $c{m}^2$

4. 169 $c{m}^2$