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Test: Application Of Heron's Formula


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10 Questions MCQ Test Mathematics (Maths) Class 9 | Test: Application Of Heron's Formula

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Test: Application Of Heron's Formula - 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​

Detailed Solution for Test: Application Of Heron's Formula - Question 1 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.
Test: Application Of Heron's Formula - Question 2

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

Detailed Solution for Test: Application Of Heron's Formula - Question 2

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

Test: Application Of Heron's Formula - 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:

Test: Application Of Heron's Formula - 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​

Test: Application Of Heron's Formula - Question 5

A square sheet whose perimeter is 32 cm is painted at the rate of Rs. 5 per m2. The cost of painting is:​

Test: Application Of Heron's Formula - Question 6

The area of an equilateral triangle of side 14 cm is

Test: Application Of Heron's Formula - Question 7

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

Test: Application Of Heron's Formula - Question 8

The base of a right angled triangle with area 300 cm2 and height 30 cm is

Test: Application Of Heron's Formula - Question 9

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

Test: Application Of Heron's Formula - 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 :

Detailed Solution for Test: Application Of Heron's Formula - Question 10
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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