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This mock test of Test: Application Of Heron's Formula for Class 9 helps you for every Class 9 entrance exam.
This contains 10 Multiple Choice Questions for Class 9 Test: Application Of Heron's Formula (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The perimeter of a triangle with two sides of length 15 cm and 12.5 cm is 40 cm. Its third side is

Solution:
A triangke has 3 sides whose perimeter is equal to the sum of the lengths of the three sides altogether. Next ,let the calculation be in. parallel i.e,12.5+15.0+x=40 27.5+x=40 x=40-27.5 x=12.5.

QUESTION: 2

Find the area of an isosceles triangle, whose unequal side is 12 cm and the perimeter of triangle, is 60 cm.

Solution:

Let the length of equal sides be x.$

Two sides are equal

Then,

x + x + 12 = 60

2x = 48

x = 24 cm

s = (a+b+c)/2

= (12+24+24)/2

60/2

= 30

Area = [s(s-a)(s-b)(s-c)]^{1/2}

= [30(30-12)(30-24)(30-24)]^{1/2}

= [30(18)(6)(6)]^{1/2}

= 36(15)^{1/2}

QUESTION: 3

The lengths of a triangle are 6 cm, 8 cm and 10 cm. Then the length of perpendicular from the opposite vertex to the side whose length is 8cm is:

Solution:

QUESTION: 4

Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on land and produce different crops to suffice the needs of their family. She divided the land in two equal parts. If the perimeter of the land is 400 m and one of the diagonals is 160 m, the area of each part is

Solution:

QUESTION: 5

A square sheet whose perimeter is 32 cm is painted at the rate of Rs. 5 per m^{2}. The cost of painting is:

Solution:

QUESTION: 6

The area of an equilateral triangle of side 14 cm is

Solution:

QUESTION: 7

An isosceles triangle has perimeter 40 cm and each of the equal sides is 15 cm. The area of the triangle is

Solution:

QUESTION: 8

The base of a right angled triangle with area 300 cm^{2} and height 30 cm is

Solution:

QUESTION: 9

The area of a scalene triangle with sides 32 cm, 34 cm and 34 cm is

Solution:

QUESTION: 10

The sides of a scalene triangle are in the ratio 3:5:7. If the perimeter of the triangle is 60 cm, then its area is :

Solution:

Given the perimeter of a triangle is 60 cm and the sides are in a ratio of 3: 5: 7

Let the sides a, b, c of a triangle be 3x, 5x, 7x respectively

So, the perimeter = 2s = a + b + c

60 = a + b + c

60 = 3x + 5x + 7x

60 = 15x

Therefore, x = 4 m

So, the respective sides are

a = 12 m

b = 20 m

c = 28 m

Now, semi perimeter s = a+b+c/2

= 12+20+28/2

= 30 cm

By using Heron’s Formula

The area of a triangle = √s(s−a)(s−b)(s−c)

= √30 x (30−12) x (30−20) x (30−28)

= 60√3

Thus, the area of a triangle is 60√3 sq.cm

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