This set of Aptitude Questions and Answers (MCQs) focuses on “Triangles – Set 2”.
1. The base of a triangle is 10 cm and height 6 cm. What will be the height of another triangle of double the area having the base 12 cm?
a) 12
b) 15
c) 10
d) 7
View Answer
Explanation: Area of first triangle = (1 / 2) * b * h
= (1 / 2) * 10 * 6
= 30cm2
Area of second triangle = 2 * area of first triangle
= 2 * 30
= 60 cm2
➩ 60 = (1 / 2) * b * h
➩ 60 = (1 / 2) * 12 * h
➩ 60 = 6 * h
➩ 60 / 6 = h
➩ 10 = h
2. The sides of a triangle are in the ratio of (1 / 2) : (1 / 3) : (1 / 6). If the perimeter is 60 cm, then what will be the length of the longest side?
a) 30
b) 20
c) 10
d) 60
View Answer
Explanation: Given,
Ratio = (1 / 2) : (1 / 3) : (1 / 6)
= 3 : 2 : 1
Perimeter = 60 cm
So, sides are = (60 * 3 / 6) cm, (60 * 2 / 6) cm, (60 * 1 / 6) cm
= 30 cm, 20cm, 10cm
The longest side is 30 cm.
3. What will be the area (in sq. cm) of an equilateral triangle if its height is 10 cm?
a) 120 / √3
b) 100 / √3
c) 90√3 / 4
d) 140 / √3
View Answer
Explanation: Let each side be x cm in length.
➩ (x / 2)2 + 102 = x2
➩ (x2 – x2 / 4) = 100
➩ 3x2 / 4 = 100
➩ x2 = 400 / 3
Area = √3 / 4 * x2
= √3 / 4 * 400 / 3
= 100 / √3 cm2
4. If the area of a square with side length z is equal to the area of a triangle with base z, then what will be the length of the altitude of the triangle?
a) 2z
b) z / 2
c) z2
d) 2z / 3
View Answer
Explanation: As we know,
Area of square = z2
Area of triangle = (1 / 2) * b * h
➩ (1 / 2) * z * h
On equating both the areas
➩ (1 / 2) * z * h = z2
➩ h = 2z
5. A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the base and the altitude of the rectangle are 20 cm and 25 cm respectively then, what will be the value of the altitude of the triangle?
a) 100 cm
b) 75 cm
c) 50 cm
d) 25 cm
View Answer
Explanation: Let the altitude of triangle be h.
Area of triangle = (1 / 2) * b * h
= (1 / 2) * 20 * h
Area of rectangle = b * l
= 20 * 25
According to the question,
➩ 20 * 25 = (1 / 2) * 20 * h
➩ h = 50 cm
6. If the side of an equilateral triangle is increased to 3 times the earlier length, then by what percentage is the area increased?
a) 500%
b) 900%
c) 400%
d) 800%
View Answer
Explanation: Let the original length be w cm.
Original area = √3 / 4 w2
New length = 3w
New area = √3 / 4 (3w)2
= 9√3 / 4 w2
Difference = 9√3 / 4 w2 – √3 / 4 w2
= 8√3 / 4 w2
%increase = ((8√3 / 4 w2) / (√3 / 4 w2)) * 100
= 800%
7. What will be the area (in sq. cm) of a triangle if the length of its sides is 128cm, 22cm and 114cm?
a) 1022.46
b) 1340
c) 1256
d) 1188
View Answer
Explanation: Perimeter of triangle = 128 + 22 + 114
= 264 cm.
Semi – perimeter = 264 / 2 cm
= 132 cm
Area = √s(s – a) (s – b) (s – c)
= √132(132 – 128) (132 – 22) (132 – 114)
= √132 (4) (110) (18)
= √1045440
= 1022.46 cm2
8. The equal sides of an isosceles triangle is 8cm and the other side is 10 cm. What will be the area of this triangle in sq. cm?
a) 37.69
b) 28.72
c) 31.22
d) 35.68
View Answer
Explanation: Perimeter = 8 + 8 + 10
= 26 cm
Semi – perimeter = 26 / 2 = 13 cm
Area of triangle = √s(s – a) (s – b) (s – c)
➩ √13 (13 – 8) (13 – 8) (13 – 10)
➩ √13 (5) (5) (3)
➩ √975
➩ 31.22 cm2
9. What will be the area (in sq. cm) of a triangle if angle A = 45 – degree, b = 10 cm and c = 15 cm?
a) 50.062
b) 53.025
c) 57.624
d) 59.782
View Answer
Explanation: Area of triangle = (1 / 2) * b * c * Sin A.
➩ (1 / 2) * 10 * 15 * (Sin45)
➩ (1 / 2) * 10 * 15 * (0.707)
➩ 53.025 cm2
10. What will be the area (in sq. cm) of a triangle of side length 20 cm?
a) 100√3
b) 144
c) 135√3
d) (100√3) / 7
View Answer
Explanation: Area of an equilateral triangle = (√3 / 4) * a2
➩ (√3 / 4) * (20)2
➩ (√3 / 4) * (400)
➩ 100√3 cm2
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