Mathematics
In triangle ABC, ∠ABC = 90°, AB = 2a + 1 and BC = 2a2 + 2a. Find AC in terms of 'a'. If a = 8, find the lengths of the sides of the triangle.
Pythagoras Theorem
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Answer
Given: In triangle ABC, ∠ABC = 90°, AB = 2a + 1 and BC = 2a2 + 2a
In Δ ABC, using Pythagoras theorem,
Hypotenuse2 = Base2 + Height2
AC2 = AB2 + BC2
= (2a + 1)2 + (2a2 + 2a)2
= 4a2 + 1 + 4a + 4a4 + 4a2 + 8a3
= 4a4 + 8a3+ 8a2 + 4a + 1
⇒ AC =
⇒ AC =
⇒ AC = 2a2 + 2a + 1
When a = 8,
AB = (2a + 1) = (2 x 8 + 1) = 16 + 1 = 17
BC = (2a2 + 2a) = (2 x 82 + 2 x 8) = 128 + 16 = 144
AC = 2a2 + 2a + 1 = 2 (8)2 + 2 x 8 + 1 = 128 + 16 + 1 = 145
Hence, AC = 2a2 + 2a + 1 and the length of AB = 17, BC = 144 and AC = 145.
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