Question:
ABC is a triangle with BC = 5. D is the foot of the perpendicular from A on BC. E is a point on CD such that BE = 3. The value of AB2-AE2+6CD is:
ABC is a triangle with BC = 5. D is the foot of the perpendicular from A on BC. E is a point on CD such that BE = 3. The value of AB2-AE2+6CD is:
Updated On: Aug 9, 2024
- 5
- 10
- 14
- 18
- 21
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The Correct Option is
Solution and Explanation
According to the question,
Using the Pythagorean theorem:
AB2 = BD2 + AD2, AE2 = DE2 + AD2
Also, BD = 3 - DE
Substituting in AB2 - AE2 + 6CD = BD2 + AD2 - DE2 - AD2 + 6CD
AB2 - AE2 + 6CD = BD2 - DE2 + 6CD = (3 - DE)2 - DE2 + 6(DE +2)
AB2 - AE2 + 6CD = 9 + DE2 - 6DE - DE2 + 6DE + 12 = 9 +12 = 21
Hence, option E is the correct answer.
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