In the right triangle, B is a point on AC such that AB + AD = BC + CD. If AB = x, BC = h and CD = d, then find x
(in term of h and d).
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x = hd/(2h + d)
Step-by-step explanation:
AB + AD = BC + CD
=> x + AD = h + d
=> AD = h + d - x
AD² = AC² + CD²
=> AD² = (AB + BC)² + CD²
=> (h + d - x)² = (x + h)² + d²
=> h² + d² + x² + 2hd - 2xh - 2xd = x² + h² + 2xh + d²
=> 2hd = 4xh + 2xd
=> hd = 2xh + xd
=> hd = x(2h + d)
=> x = hd/(2h + d)
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