Discussion

Explanation:

In right triangle ABC, since AB and BC have to be integers it has to be a pythagorean triplet.
Since, AC = 17, the applicable pythagorean triplet is 8, 15 and 17.
Now, (AB, BC, AC) = (8, 15 and 17) or (15, 8 and 17).

In ∆ABC and ∆BCD
∠ABC = ∠BCD, &
∠BAC = ∠CBD
∴ ∆ABC is similar to ∆BCD

Case 1: (AB, BC, AC) = (8, 15 and 17)
Area of ABCArea of BCD = ABBC2 = 8152 = 64225

Case 2: (AB, BC, AC) = (15, 8 and 17)
Area of ABCArea of BCD = ABBC2 = 1582 = 22564

Hence, option (d).

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