Question

A triangle has sides 35 cm, 54cm,61cm, long. Find its area. Also find the smallest of its altitude​

Answer 1

Step-by-step explanation:

As all the sides of triangle are different, so triangle is scalene.

Area of a scalene triangle is calculated by the Helen's formula

A = √([s(s - a)(s - b)(s - c)]

Here s is the semi(half) perimeter.

s = 35+54+61 / 2

s = 150 / 2

s = 75

A = √[75(75 - 35)(75 - 54)(75 - 61)]

A = √(75 × 40 × 21 × 14)

A = 939.15 cm²

We know that,

area of general Triangle = 1/2×b×h

939.15 × 2 / b = h

h = 1878.3 / b

Here, the largest breadth will have the smallest altitude.

h = 1878.3 / 61

h = 30.79 cm

So smallest altitude = 30.79cm

Answer 2

Step-by-step explanation:

in the given triangle we have sides-35cm 54cm 61cm

here we can say that it is a scalene triangle now area of scalene triangle is √s(s-a)(s-b)(s-c)

s=a+b+c/2

s=35+54+61/2=75

area=√75(75-35)(75-54)(75-61)

area=√75×40×21×14

area=√882000

area=