Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

In \( \Large \triangle ABC \), D and E are points on sides AB and AC, such that \( \Large DE \parallel BC \). If AD = x, DB = x - 2, AE = x + 2 and EC = x - 1, then the value of x is

A) 4
B) 2
C) 1
D) 8

Correct Answer:

A) 4

Description for Correct answer:

\( \Large \because DE \parallel BC \)

\( \Large \therefore \frac{AD}{DB} = \frac{AE}{EC} \)

=> \( \Large \frac{x}{x-2} = \frac{x+2}{x-1} \)

=> \( \Large x^{2} - x = x^{2} - 4 \)

=> x = 4

Part of solved Geometry questions and answers : >> Elementary Mathematics >> Geometry

Comments

Similar Questions

1). In \( \Large \triangle ABC \), AB = AC and D is a point on AB, such that AD = DC = BC. Then \( \Large \angle BAC \), is

A). \( \Large 40 ^{\circ} \)

B). \( \Large 45 ^{\circ} \)

C). \( \Large 30 ^{\circ} \)

D). \( \Large 36 ^{\circ} \)

2). In a \( \Large \triangle ABC \), \( \Large \angle A \) : \( \Large \angle B \) : \( \Large \angle C \) = 2 : 3 : 4. A line CD drawn parallel to AB, then \( \Large \angle ACD \) is

A). \( \Large 80 ^{\circ} \)

B). \( \Large 20 ^{\circ} \)

C). \( \Large 40 ^{\circ} \)

D). \( \Large 60 ^{\circ} \)

3). The mid-points of AB and AC of a \( \Large \triangle ABC \) are respectively X and Y. If BC + XY = 12 units, then the value of BC - XY is

A). 6

B). 8

C). 4

D). 12

4). In the figure given below, \( \Large \angle ABC \) = \( \Large \angle AED \) = \( \Large 90 ^{\circ} \)

Consider the following statements
I. ABC and ADE are similar triangles.
II. The four points B, C, E and D may lie on a circle.
Which of the above statements is/are correct?

A). Only I

B). Only II

C). Both I and ll

D). Neither I nor ll

5). In a \( \Large \triangle ABC \), \( \Large \angle BCA = 60 ^{\circ} \) and \( \Large B^{2} = BC^{2} + CA^{2} + X \). What is the value of X?

A). \( \Large \left(BC\right) \left(CA\right) \)

B). \( \Large - \left(BC\right) \left(CA\right) \)

C). \( \Large \left(AB\right) \left(BC\right) \)

D). Zero

6). In a \( \Large \triangle ABC \), XY is drawn parallel to BC, cutting sides at X and Y, where AB = 4.8 cm, BC = 7.2 cm and BX = 2 cm. What is the length of XY?

A). 4 cm

B). 4.1 cm

C). 4.2 cm

D). 4.3 cm

7). The angles \( \Large x ^{\circ} \), \( \Large a ^{\circ} \), \( \Large c ^{\circ} \) and \( \Large \left( \pi - b\right) ^{\circ} \) are indicated in the figure given below. Which one of the following is correct?

A). x = a + c - b

B). x = b - a - c

C). x = a + b + c

D). x = a - b + c

8). In the figure given below, \( \Large YZ \parallel MN \), \( \Large XY \parallel \ LM \ and \ XZ \parallel LN\) Then, MY is

A). the median of ALMN

B). the angular bisector of ALMN

C). perpendicular to LN

D). perpendicular bisector ol LN

9). In the figure given below, AB is parallel to CD \( \Large AB \parallel CD \), \( \Large \angle ABC \) = \( \Large 65 ^{\circ} \), \( \Large \angle CDE \) = \( \Large 15 ^{\circ} \) and AB = AE. What is the value of \( \Large \angle AEF \)?

A). \( \Large 30 ^{\circ} \)

B). \( \Large 35 ^{\circ} \)

C). \( \Large 40 ^{\circ} \)

D). \( \Large 45 ^{\circ} \)

10). External angle of a regular polygon is \( \Large 72^{\circ} \). Find the sum of all the internal angles of it.

A). \( \Large 360 ^{\circ} \)

B). \( \Large 480 ^{\circ} \)

C). \( \Large 352 ^{\circ} \)

D). \( \Large 540 ^{\circ} \)