In triangle ABC the angle at A is 90°, and AD is the altitude from A to the hypotenuse BC, with D on BC. If BD = 4 and DC = 9, what is the length of AB?

Question

Accepted Answer

2√13. BC = BD + DC = 13. Triangle ABD is similar to triangle CBA, which gives AB² = BD × BC = 4 × 13 = 52. So AB = √52 = 2√13. (For reference, AD = √(4 × 9) = 6 and AC = √(9 × 13) = 3√13.)

In triangle ABC the angle at A is 90°, and AD is the altitude from A to the hypotenuse BC, with D on BC. If BD = 4 and DC = 9, what is the length of AB?

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