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Question 1: In a $△$ ABC, D and E are two points on sides AB and AC such that DE is parallel to BC and AD : DB = 2 : 1. If AE = 8 cm, then find the length of AC.

a) 12 cm
b) 10 cm
c) 16 cm
d) 20 cm

Solved Examples: Triangles | Quantitative Aptitude for SSC CGL

View Answer

Answer (A)

Solved Examples: Triangles | Quantitative Aptitude for SSC CGL

Here, Solved Examples: Triangles | Quantitative Aptitude for SSC CGL and AE = 8 cm

Solved Examples: Triangles | Quantitative Aptitude for SSC CGL
Here, AC = AE+EC = 4+8 = 12 cm

Question 2: In a $△$ ABC, Points D and E are on sides AB and AC such that DE is parallel to BC and AD : DB = 3 : 1 and AE = 18 cm. Then find AC.

a) 26 cm
b) 24 cm
c) 28 cm
d) 32 cm

View Answer

Answer (B)

Given, DE is parallel to BC.
Then

Here,
AE= 18 cm
Solved Examples: Triangles | Quantitative Aptitude for SSC CGL

⇒ EC = 6 cm
AC = AE+EC = 6+18 = 24 cm

Question 3: In a $△$ ABC, points D and E are on the sides of AB and AC respectively such that DE is parallel to BC and AD : AB = 2 : 5 and AE = 4 cm. Then find AC.

a) 10 cm
b) 14 cm
c) 12 cm
d) 9 cm

View Answer

Answer (B)

Given, DE is parallel to BC.
Then, Solved Examples: Triangles | Quantitative Aptitude for SSC CGL

Here, Solved Examples: Triangles | Quantitative Aptitude for SSC CGL

AE= 4 cm
Solved Examples: Triangles | Quantitative Aptitude for SSC CGL

⇒ EC = 10 cm
AC = AE+EC = 4+10 = 14 cm

Question 4: The coordinates of the vertices of a right-angled triangle are A (6, 2), B(8, 0) and C (2, -2). The coordinates of the orthocentre of triangle PQR are

a) (2, -2)
b) (2, 1)
c) (6, 2)
d) (8, 0)

View Answer

Answer (C)
Given that the coordinates of a right-angled triangle are A (6, 2), B(8, 0) and C (2, -2).
We know that the distance between two points(a, b) &(c, d) is
Solved Examples: Triangles | Quantitative Aptitude for SSC CGL

Therefore, angle A is right angled.
Since it is a right angled triangle, the 2 sides adjacent to the right angle will be altitudes. The third altitude must meet at the vertex at which these 2 sides meet.
Hence, the vertex that contains the right angle is the orthocentre. From the points given, we can clearly see that (6, 2) is the orthocentre. Option C is the right answer.

Question 5: find the area of an equilateral triangle if the height of the triangle is 24 cm.
a) Solved Examples: Triangles | Quantitative Aptitude for SSC CGL
b)
c)
d)

View Answer

Answer (A)
Given,
AD = 24 cm and ABC is an equilateral triangle
In an equilateral triangle all the angles are equal to 60°

Solved Examples: Triangles | Quantitative Aptitude for SSC CGL

Question 6: Three sides of a triangular meadow are of length 28 m, 45 m and 53 m long respectively. Find the cost of sowing seeds(in rupees per sq.m) in the meadow at the rate of 12 rupees per sq.m.

a) 7560
b) 6860
c) 7960
d) 7860

View Answer

Answer (A)
Given the sides of triangle are 28 m, 45 m and 53 m
Since, Solved Examples: Triangles | Quantitative Aptitude for SSC CGL

=> The given sides are of right angled triangle as, Solved Examples: Triangles | Quantitative Aptitude for SSC CGL

where a, b, c are the sides of the triangle

.=> Area of triangular field Solved Examples: Triangles | Quantitative Aptitude for SSC CGL

=> Cost of sowing seeds =

Question 7: In a triangle PQR, internal angular bisectors of $∠ 𝑄$ and $∠ 𝑅$ intersect at a point O. If $∠ 𝑃$ = $110 \circ$ then what is the value of $∠ 𝑄 𝑂 𝑅$ ?
a) $125 \circ$
b) $135 \circ$
c) $145 \circ$
d) $115 \circ$

View Answer

Answer (C)

Sum of angles in a triangle=180
2x+2y+110=180
2x+2y=70
x+y=35
Similarly in the triangle QOR we have

Solved Examples: Triangles | Quantitative Aptitude for SSC CGL

Question 8: In a triangle XYZ, XA is the angle bisector onto YZ. If the semiperimeter of the triangle is 12 and XY=12 ,YZ=6 then what is the ratio of YA:AZ ?

a) 2:3
b) 2:1
c) 1:2
d) 3:2

View Answer

Answer (B)

In triangle XYZ we have s=12
(x+y+z)/2 =12
x+y+z=24
12+6+y=24
y=6
Angle bisector divides the opposite side in the ratio of other sides i.e
XY/XZ=YA/AZ
YA/AZ=12/6
YA/AZ=2:1

Question 9: In a triangle ABC, AX is the angle bisector onto BC. If the semiperimeter of the triangle is 9 and AB=4 ,BC=6 then what is the ratio of BX:XC ?

a) 2:3
b) 2:1
c) 1:2
d) 3:2

View Answer

Answer (C)

In triangle ABC we have s=9
(a+b+c)/2 =9
a+b+c=18
4+6+b=18
b=8
Angle bisector divides the opposite side in the ratio of other sides i.e
AB/AC=BX/XC
BX/XC=4/8
BX/XC=1:2

Question 10: In an equilateral triangle,if h-R=15 cm where h=height of the triangle and R=circumradius then what is the area of the triangle ?

a) Solved Examples: Triangles | Quantitative Aptitude for SSC CGL
b)
c)
d)

View Answer

Answer (D)

In an equilateral triangle,all the points such as orthocentre,centroid,circumcenter coincide.
Let the triangle be PQR and the circumcentre be O. let median intersect QR at A
Centroid divides median in the ratio 2:1.PA=h,OA=R
OA=15 cm
Therefore (PO:OA)=2:1
PO:15=2:1
PO=30
PA=PO+OP
PA=30+15
PA=45
PA is also the altitude using it side of the triangle can be calculated.

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FAQs on Solved Examples: Triangles - Quantitative Aptitude for SSC CGL

1. What are the different types of triangles based on their angles?

Ans. The different types of triangles based on their angles are equilateral, isosceles, and scalene triangles.

2. How do you calculate the area of a triangle?

Ans. The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.

3. What is the Pythagorean theorem and how is it used in triangles?

Ans. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. It is commonly used to find the length of a side in a right triangle.

4. How can you determine if three given side lengths form a triangle?

Ans. To determine if three given side lengths form a triangle, you can use the triangle inequality theorem which states that the sum of any two sides of a triangle must be greater than the third side.

5. How do you find the missing angle in a triangle?

Ans. To find the missing angle in a triangle, you can use the fact that the sum of all angles in a triangle is always 180 degrees. Subtract the known angles from 180 degrees to find the missing angle.

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