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Triangles - Aptitude MCQ Questions and Solutions with Explanations

Triangles MCQ Questions and answers with easy and logical explanations.Arithmetic Ability provides you all type of quantitative and competitive aptitude mcq questions on Triangles with easy and logical explanations. Triangles MCQ is important for exams like Banking exams,IBPS,SCC,CAT,XAT,MAT etc. Page-5 section-2

Each section contains 100 MCQs on Triangles .
41
In a right angled triangle ΔDEF, if the length of the hypotenuse EF is 12 cm, then the length of the median DX is:
Discuss
Answer & Solution
Answer: Option C
Solution:
Median of right angle
$$\eqalign{ & = \frac{{EF}}{2} \cr & = \frac{{12}}{2} \cr & = 6\,{\text{cm}} \cr} $$
42
In an equilateral triangle ABC, G is the centroid. Each side of the triangle is 6 cm. The length of AG is:
Discuss
Answer & Solution
Answer: Option C
Solution:
Triangles mcq solution image
In Equilateral triangle
$$\eqalign{ & AG:GD = 2:1 \cr & AD = \frac{{\sqrt 3 }}{2}a \cr & AD = \frac{{\sqrt 3 }}{2} \times 6 \cr & AD = 3\sqrt 3 \cr & 3 \to 3\sqrt 3 \cr & 1 \to \sqrt 3 \cr & AG = 2\,{\text{unit}} = 2\sqrt 3 \,{\text{cm}} \cr} $$
43
In case of an acute angled triangle, its orthocenter lies:
Discuss
Answer & Solution
Answer: Option A
Solution:
In acute angled triangle orthocenter is always inside the triangle
44
If the measure of the angles of a triangle are in the ratio 1 : 2 : 3 and if the length of the smallest side of the triangle is 10 cm, then the length of the longest side is:
Discuss
Answer & Solution
Answer: Option A
Solution:
Let angle = x, 2x, 3x
x + 2x + 3x = 180
(∵ Sum of internal angle of a Δ)
6x = 180°
x = 30°
So, angle = 30, 60, 90
Smallest side of Δ
= 1 unit
= 10 cm
Largest side of Δ
= 2 units
= 20 cm
45
In a triangle ABC, ∠A = 70°, ∠B = 80° and D is the incenter of ΔABC, ∠ACB = 2x° and ∠BDC = y°. The values of x and y, respectively are:
Discuss
Answer & Solution
Answer: Option B
Solution:
Triangles mcq solution image
∠C = 180 - (∠A + ∠B)
∠C = 180 - 150
2x = 30
x = 15°
Triangles mcq solution image
∠BDC = 90° + $$\frac{1}{2}$$ ∠A
∠BDC = 90° + $$\frac{1}{2}$$ × 70°
∠BDC = 90° + 35°
∠BDC = 125°
So value of x and y are = 15°, 125°
46
In ΔABC, AC = BC and ∠ABC = 50°, the side BC is produced to D so that BC = CD then the value of ∠BAD is:
Discuss
Answer & Solution
Answer: Option C
Solution:
Triangles mcq solution image
In ΔABC
∠B = ∠A = 50°
∠ACD = 50° + 50°
∠ACD = 100°
∠ACD is the external angle or ΔABC
∠ACD + ∠CAD + ∠ADC = 180°
∠CAD = ∠ADC
∵ AC = CD
2∠CAD = 180 - 100
∠CAD = 40°
∠BAD = 50° + 40°
∠BAD = 90°
47
An equilateral triangle of side 6 cm is inscribed in a circle. Then radius of the circle is:
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & R = \frac{a}{{\sqrt 3 }} \cr & R = \frac{6}{{\sqrt 3 }} \cr & R = 2\sqrt 3 \,{\text{cm}} \cr} $$
48
If ΔPQR and ΔLMN are similar and 3PQ = LM and MN = 9 cm, then QR is equal to:
Discuss
Answer & Solution
Answer: Option D
Solution:
Triangles mcq solution image
$$\eqalign{ & \frac{{PQ}}{{LM}} = \frac{{QR}}{{MN}} = \frac{{PR}}{{LN}} \cr & \left( {\vartriangle PQR\,{\text{and}}\,\vartriangle LMN\,{\text{are}}\,{\text{similar}}} \right) \cr & \frac{{PQ}}{{LM}} = \frac{{QR}}{{MN}} \cr & \frac{1}{3} = \frac{{QR}}{9} \cr & QR = 3\,{\text{cm}} \cr} $$
49
In a ΔABC, ∠A + ∠B = 75° and ∠B + ∠C = 140°, then ∠B is:
Discuss
Answer & Solution
Answer: Option B
Solution:
∠A + ∠B = 75° . . . . . . (i)
∠B + ∠C = 140° . . . . . (ii)
(we know)
∠A + ∠B + ∠C = 180° . . . . . . (iii)
from equation (i) & (iii)
∠C = 105° . . . . . . . . . . . . . . . (iv)
from equation (ii) & (iv)
∠B = 35°
50
ABC is an isosceles triangle where AB = AC which is circumscribed about a circle. If P is the point where the circle touches the side BC, then which of the following is true?
Discuss
Answer & Solution
Answer: Option A
Solution:
Triangles mcq solution image
here given that = AB = AC
AQ + BQ = AR + RC
we know that
BQ = PB & PC = RC
AQ + PB = AR + PC
also AQ = AR
AR + PB = AR + PC
PB = PC