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Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Class 9 MCQ


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20 Questions MCQ Test - Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics

Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics for Class 9 2024 is part of Class 9 preparation. The Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics questions and answers have been prepared according to the Class 9 exam syllabus.The Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics MCQs are made for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics below.
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Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 1

The base of a right angled triangle is 5 metres and hypotenuse is 13 metres. Its area will be:

Detailed Solution for Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 1

Hypotenuse = √(base2+height2)
height2 = Hypotenuse- base2
height = √(132 - 52)
⇒ √144 ⇒ 12

Area of the triangle = 1/2(base*height)
=1/2(5 x 12 ) m2
= 30m2

Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 2

The sides of a triangular board are 13 metres, 14 metres and 15 metres. The cost of painting it at the rate

of Rs. 8.75 per m2 is

Detailed Solution for Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 2

s = (13 + 14 + 15 ) / 2 = 21, 
s-a = 8 , 
s-b = 7, 
s-c= 6

∴ Area to be painted = √ [s(s-a) (s-b) (s-c)]
=√ [21 * 8 * 7 * 6] m2
= 84 m2
∴ Cost of painting = Rs. (84 * 8.75) = Rs. 735

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Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 3

The area of an equilateral triangle whose side is 8 cm, is

Detailed Solution for Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 3
Area of an equilateral triangle = √3/4 x (side)^2

Given side = 8 cm

So, area = (√3/4) x 8 x 8
      area   = 16√3 cm^2
Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 4

The length of each side of an equilateral triangle having an area of 4 √3 cm2, is :

Detailed Solution for Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 4
The area of an equilateral triangle of side a = [(a^2)/2]sin 60 or

4*3^0.5 = [(a^2)/2]*3^0.5/2, or

2*2*4*3^0.5 = a^2 *3^0.5 or

a = 4 cm.

Hence the side of the equilateral triangle = 4 cm.
Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 5

The area of a triangle is 150 cm2 and its sides are in the ratio 3 : 4 : 5. What is its perimeter?

Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 6

The altitude of an equilateral triangle of side 2 √3 cm is :

Detailed Solution for Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 6
Area of triangle =√3/4 ×(2√3)²= ½BH
= 3√3 cm² = ½ 2√3 ×H = H = 3√3 × 2 / 2√3 = H = 3×2/2 =H =3 cm
Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 7

In a triangle ABC, BC = 5 cm, AC = 12 cm and AB = 13 cm. The length of the altitude drawn from B on AC is :

Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 8

A triangle of area 9 × y cm2 has been drawn such that its area is equal to the area of an equilateral triangle of side 6 cm. Then, the value of y is

Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 9

In Δ PQR, side QR = 10 cm and height PM = 4.4 cm. If PR = 11 cm, then altitude QN equals :

Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 10

The area of a right angled triangle is 30 cm2 and the length of its hypotenuse is 13 cm. The length of the shorter leg is:

Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 11

Area of a square with side x is equal to the area of a triangle with base x. The altitude of the triangle is :

Detailed Solution for Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 11

Area of triangle = Δ = 1/2 ​* (base) * (height) 

Let altitude of the triangle is =h
and base = x

Given the area of a triangle with base x is equal to the area of a square with side x

We know Δ = x2
⇒ Δ = 1/2 * x * (height) = x2
⇒ h = 2x

Height/altitude of triangle is 2x.

Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 12

A plot of land is in the shape of a right angled isosceles triangle. The length of the hypotenuse is 50 √2 m.The cost of fencing it at Rs. 3 per metre will be :

Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 13

The perimeter of an isosceles triangle is equal to 14 cm, the lateral side is to the base in the ratio 5 : 4. The area of the triangle is

Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 14

If the area of an equilateral triangle is 24√3 sq. m, then its perimeter is :

Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 15

The ratio of the area of a square of side a and equilateral triangle of side a, is :

Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 16

If every side of a trianlge is doubled, then increase in the area of the triangle is :

Detailed Solution for Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 16

Let the sides of the given triangle be a, b and c.


 

Given that the sides of the triangle are doubled.

That is sides of new triangle are 2a, 2b and 2c.


 

Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 17

If the altitude of an equilateral triangle is √6 , then its area is :

Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 18

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

Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 19

If an equilateral triangle of area X and a square of area Y have the same perimeter, then :

Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 20

A square and an equilateral triangle have equal perimeters. If the diagonal of the square is 12√2  cm, then the area of the triangle is :

Detailed Solution for Heron's Formula - Olympiad Level MCQ, Class 9 Mathematics - Question 20
Diagonal of a square = side (root 2)
12 (root 2) = side (root 2)
Side = 12cm
P of square = 12 x 4 = 48
P of triangle = 3 x a = 48
                    => a = 16
A of equilateral triangle = (root 3)/4 (a^2)
                                      = (root 3) 64
                                      = 64√3cm^2
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