Triangles

Q.

Find the perpendicular distance of a right triangle's hypotenuse from its opposite vertex if the base and attitude of the triangle is 24 cm and 10 cm respectively.

1. 1 cm

2. 14 cm

3. Insufficient data

4. 120/13 cm

5. 32/3 cm

Q. In a triangle ABC, M is the mid-point of BC. If $\angle$AMB = 45${}^{\circ }$, and $\angle$ACM = 30${}^{\circ }$, then $\angle$BAM is ($\angle$B is not obtuse)

1. 30˚
2. 45˚
3. < 30˚
4. ≥ 45˚

Q. In triangle ABC, G is the centroid, AB = 15 cm, BC = 18 cm and AC = 25 cm. Find GD, where D is the mid - point of BC:

1. $\frac{1}{3}\sqrt{86}cm$
2. $\frac{2}{3}\sqrt{86}cm$
3. $\frac{8}{3}\sqrt{15}cm$
4. $Noneofthese$

Q. In the given figure, EADF is a rectangle and ABC is a triangle whose vertices lie on the sides of EADF. AE = 22, BE =16, CF = 16, CF = 16 and BF = 2. Find the length of the line joining the
mid-points of the sides AB and BC.
(CAT 1997)

1. 5
2. 3.5
3. none of these
4. 

Q. The base of a triangular field is three times its height. If the cost of cultivating the field at Rs 36.72 per hectare is Rs 495.72, then find its base and height.

1. 950 m, 350 m
2. 800 m, 500 m
3. 900 m, 300 m
4. 860 m, 540 m
5. None of these

Q. In the figure below, AB = BC = CD = DE = EF = FG = GA. Then, $\angle DAE$ is approximately

1. ${25}^{\circ }$
2. ${15}^{\circ }$
3. ${30}^{\circ }$
4. ${20}^{\circ }$

Q. In the given figure, AD is the external bisector of $\angle EAC,$ intersects BC produced to D. If AB = 12 cm, AC = 8 cm and BC = 4 cm, find CD.

1. 10 cm
2. 6 cm
3. 8 cm
4. 9 cm

Q. In the figure (not drawn to scale) given below, P is a point on AB such that AP: PB = 4:3. PQ is parallel to AC and QD is parallel to CP. In $\Delta ARC,\angle ARC={90}^{\circ }$, and in $\Delta PQS,\angle PSQ={90}^{\circ }$. The length of QS is 6 cms. What is ratio AP: PD?

1. 10 : 3
2. 2 : 1
3. 7 : 3
4. 8 : 3

Q. In the figure, AD = 12 cm, AB = 20 cm and AE = 10 cm. Find EC:

1. 14 cm
2. 8 cm
3. 15 cm
4. 10 cm

Q. Based on the figure below, what is the value of x, if y = 10

1. 10
2. 11
3. None of these
4. 12

Q.

A triangle has sides 5 cm, 12 cm and 13 cm. Find the length of the perpendicular from the opposite vertex to the side whose length is 13 cm.

1. 5.1 cm

2. 4 cm

3. 4.8 cm

4. 4.6 cm

Q. The sides of a triangle are in the ratio 3 : 4 : 5. If its perimeter is 36 cm, then the area of the triangle is ___.

1. None of these
2. $57c{m}^2$
3. $64c{m}^2$
4. $54c{m}^2$
5. $56.5c{m}^2$

Q. In the given figure, P and Q are the mid-points of AC and AB. Also, PG = GR and HQ = HR. What is the ratio of area of $\Delta PQR$ : area of $\Delta ABC$ ?

1. $\frac{1}{2}$
2. $Noneoftheabove$
3. $\frac{2}{3}$
4. $\frac{3}{5}$

Q. $\Delta ABC$ is a right angled at A and AD is the altitude to BC. If AB = 7 cm and AC = 24 cm. Find the ratio of AD to AM, where M is the midpoint of BC:

1. $25:41$
2. $\frac{625}{336}$
3. $32:41$
4. $\frac{336}{625}$

Q. In the equilateral triangle ABC, AD = DE = BE, D and E lies on the AB. If each side of the triangle (i.e., AB, BC and AC) be 6 cm, then the area of the shaded region is :

1. $Noneoftheabove$
2. $5\sqrt{3}c{m}^2$
3. $9c{m}^2$
4. $6\sqrt{3}c{m}^2$

Q. In a right angled triangled ABC, CD is the perpendicular on the hypotenuse AB. Which of the following is correct ?

1. $BD=\frac{BC\times BC}{AB}$
2. $CD=\frac{AC\times BC}{AB}$
3. $AD=\frac{AC\times AC}{AB}$
4. $Alloftheabove$

Q. In the adjoining figure, a star is shown, What is the sum of the angles A, B, C, D and E?

1. $Ca{n}^{\prime }tbedetermined$
2. ${240}^{\circ }$
3. ${120}^{\circ }$
4. ${180}^{\circ }$

Q. In a triangle ABC, O is the centre of incircle PQR, $\angle BAC={65}^{\circ },\angle BCA={75}^{\circ }$, find $\angle ROQ$:

1. ${80}^{\circ }$
2. ${120}^{\circ }$
3. ${140}^{\circ }$
4. can't be determined

Q. In the given triangle ABC, CD, BF and AE are the altitudes. If the ratio of CD : AE : BF = 2 : 3 : 4, then the ratio of AB : BC : CA is :

1. 6 : 4 : 3
2. 4 : 3 : 2
3. 2 : 3 : 4
4. 4 : 9 : 16

Q.

Find the length of the rectangular field if its perimeter is $240m$ and breadth is $52m$

Q. In the triangle ABC, BC = CD and $(\angle ABC-\angle BAC)={30}^{\circ }$. The measure of $\angle ABD$ is :

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${15}^{\circ }$
4. $Ca{n}^{\prime }tbedetermined$

Q. If $x^2+y^2+z^2=xy+yz+zx,$ then the triangle is :

1. Isosceles
2. Scalene
3. Right angled
4. Equilateral

Q. In the triangle ABC, MN is parallel to AB. Area of trapezium ABNM is twice the area of triangle CMN. What is ratio of CM : AM ?

1. $\frac{\sqrt{3}-1}{2}$
2. $\frac{\sqrt{3}+1}{2}$
3. $Noneofthese$
4. $\frac{1}{\sqrt{3}+1}$

Q.

Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is___

Q.

In a right angle triangle ABC, $\angle A$ is right angle DE is parallel to the hypotenuse BC and the length of DE is 65% the length of BC, what is the area of $\Delta ADE,$ if the area of $\Delta ABC$ is $68c{m}^2$ ?

1. $41.6c{m}^2$

2. None of the above

3. $27.83c{m}^2$

4. $28.73c{m}^2$

Q. A triangle ABC has 2 points marked on the side BC, 5 points marked on the side CA and 3 points marked on side AB. None of these marked points is coincident with the vertices of the triangle ABC. All possible triangles are constructed taking any three of these points and the points A, B, C as the vertices. How many new triangles have atleast one vertex common with the triangle ABC?

1. 127

2. 256

3. 237

4. 207

Q. The perimeter of a right angled triangle is 90 cm and its hypotenuse is 39 cm. Find its other sides.

1. 30 cm, 10 cm
2. 36 cm, 15 cm
3. 48 cm, 20 cm
4. 38 cm, 13 cm
5. None of these

Q. An equilateral triangle plate is to be cut into n number of identical small equilateral triangle plates. Which of the following can be a value of n?

1. 216
2. 256
3. 312
4. 212

Q.

In triangle ABC, side AC and the perpendicular bisector of side BC meet at point D and BD bisects $\angle ABC.$ If AD = 9 AND DC = 7.Find area of $\Delta$ ABD

1. 
   

2. 25

3. 
   

4. 
   

Q. In the figure (not drawn to scale) given below, if AD=CD=BC, and $\angle BCE={96}^{\circ }$, how much is $\angle DBC$ ?

1. ${84}^{\circ }$
2. ${64}^{\circ }$
3. ${32}^{\circ }$
4. cannot be determined