ABC is a triangle with BC = 5. D is thefoot of the perpendicular from A on BC. E is a point on CD such that BE = 3.
The value of AB2 - AE2 + 6CD is:
Explanation:
Given, BC = 5 and BE = 3
In △ABD ⇒ AB2 = AD2 + BD2 ...(1) In △AED ⇒ AE2 = AD2 + DE2 ...(2)
(1) - (2) ⇒ AB2 - AE2 = BD2 - DE2 ⇒ AB2 - AE2 = x2 - (3 - x)2 ⇒ AB2 - AE2 = x2 - 9 - x2 + 6x ⇒ AB2 - AE2 = - 9 + 6x
We need to find AB2 - AE2 + 6CD = (-9 + 6x) + 6 × (5 - x) = -9 + 6x + 30 - 6x = 21
Hence, option (e).
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