Engineering
Mathematics
Basic Rules of Properties of Triangle
Question
The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side?
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Solution
Let sides a, b, c with a < b < c
2b = a + c
c2 = a2 + b2
Area = ab = 24 ⇒ ab = 48.
a2 + b2 = (2b – a)2 = 4b2 + a2 – 4ab
⇒ 3b2 = 4 × 48 ⇒ b2 = 64 ⇒ b = 8.
a = 6.