Proportion in Similar Triangles

Q. In triangle ABC, DE is parallel to AB. If CD = 3 cm, EC = 4 cm, BE = 6 cm, then DA is equal to

1. 5 cm
2. 3 cm
3. 4 cm
4. 4.5 cm

Q.

Two ladders are leaning against a wall in such a way that they both make the same angle with the ground. If the ladder measuring 20 feet reaches 15 ft up the wall, how much further up the wall does the ladder measuring 30 feet reach?

1. 7.5 feet

2. 22.5 feet

3. 30 feet

4. 15 feet

Q.

In the given figure, $D$ is the mid-point of $BC$, then the value of $\frac{\cot \left(y°\right)}{\cot \left(x°\right)}$ is

1. $2$

2. $\frac{1}{4}$

3. $\frac{1}{3}$

4. $\frac{1}{2}$

Q. In the given figure, D is the mid-point of AB and $PC=\frac{1}{2}AP=3$ cm. If $AD=DB=4$ cm and $DE||BP$ , then AE is:

1. 4 cm
2. 8 cm
3. 3 cm
4. 5 cm

Q.

On a sunny day, a person who is 5 feet tall casts a 3 feet long shadow. Find the height of a nearby flagpole which casts a 12 feet long shadow.

1. 10 feet

2. 25 feet

3. 15 feet

4. 20 feet

Q.

$△$ ABC a right-angled triangle, find the length of BD assuming $△ABC\sim △BDC$

1. 8.6 units

2. 9.6 units

3. 10 units

4. 6 units

Q.

In the figure above, find the missing length DE assuming BC is parallel to DE.

1. 24 cm

2. 20 cm

3. 10 cm

4. 12 cm

Q.

Find the value of x.

1. 2 cm

2. 4 cm

3. 8 cm

4. 6 cm

Q.

Consider the figure given below where $△ABC$ and $△DEF$ are similar. Find the length of the missing side x.

1. $\frac{1}{9}$

2. 9

3. 36

4. $\frac{1}{36}$

Q.

In the above figure , find the value of $x$.

1. 4 cm

2. 12 cm

3. 20 cm

4. 8 cm

Q. $△ABC$ is similar to $△XYZ$. Length of $AB,BC,CA$ are 3 cm, 4 cm and 5 cm respectively. Find the length of $YZ$ and $XZ$ if $XY=9cm$.

1. 6 cm and 8 cm
2. 9 cm and 12 cm
3. 9 cm and 15 cm
4. 12 cm and 15 cm

Q.

If x:y::3:5, find the ratio 4x+9y:8x+9y.

1. 23:19

2. 19:23

3. 3:5

4. 5:3

Q.

In the angle shown below, as the distance (represented by a, x ) from the vertex of the angle changes, the height (represented by b, h) also changes.

Given that $h\propto x$, find the constant of proportionality.

1. $\frac{a}{b}$

2. 1

3. $\frac{b}{2}$

4. $\frac{a}{4}$

Q.

Find n.

1. 10

2. 12

3. 18

4. 6

Q.

If $△ABC$ and $△PQR$ in the below figure are similar, find the missing length x and the measure of $\angle R$

1. 20 cm, 60°

2. 20 cm, 22 °

3. 22 cm, 20°

4. 25 cm.100°

Q.

From the figure, Find (x).

1. 16 units

2. 20 units

3. 10 units

4. 5 units

Q. The ratio in which line $3x+4y=2$ divides the distance between $3x+4y=7$ and $6x+8y+19=0$ is:

1. $10:23$
2. $23:10$
3. $13:10$
4. $10:13$

Q. Match the similar triangles whose sides are given in cm.

1. 10, 24, 26
2. 9, 12, 15
3. 4.5, 20, 20.5

Q. $\Delta$ABC and $\Delta$PQR are similar triangles. If AB = 12 cm, BC = 14 cm, AC = 4 cm, PQ = 6 cm, QR = (x + 2) cm, PR = (y + 3) cm, find the values x and y.
[3 Marks]

Q.

If $△ABC$ and $△PQR$ in the below figure are similar, find the missing length x and the measure of $\angle R$

Q. Number of asymptotes of the function, $f\left(x\right)=\frac{x+3}{x^2+9}$ is

1. $1$
2. $3$
3. $0$
4. $2$

Q.

In the above figure, what is the length of EF given that $\angle DEF=90°$ ?

1. 20 cm

2. 10 cm

3. 15 cm

4. 5 cm

Q. $ABC$ is a triangle. Locate a point in the interior of $△ABC$ which is equidistant from all the vertices of $△ABC$.

Q.

In a right angled triangle, the ratio of the shorter sides is 2:3. Find the ratio of the hypotenuse of the triangle to its perimeter. $(Assume\sqrt{13}=3.5)$

Q.

In the angle shown below, as the distance (represented by a, x) from the vertex of the angle changes, the height (represented by b, h) also changes.

Given that $h\propto x$, find the constant of proportionality.

Q. Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers the ratio is 4 : 5. Find the numbers