Question

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

Answer 1

Answer:

Area is 2100 cm and smallest altitude is 68.85cm

Step By Step Explanation

Let a=35cm

b=54cm

c=61cm

s= 2

a+b+c = 2 +35+54+61= 2÷150

=75cm

Area of triangle =

s(s−a)(s−b)(s−c)

= 75(75−35)(75−54)(75−61)

= 75×40×21×14

= 25×3×4×10×7×3×7×2

= 5×5×3×3×2×2×7×7×2×2×5×5

=5×3×2×7×2×5

=30×70

=2100cm

Smallest altitude will be the altitude on greatest side

So, Area of triangle =2100

⇒ 21 ×61×h=2100

h= 61

2100×2⇒

h= 61

4200 cm

h=68.85cm(approx).