Question

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).
​

Answer 1

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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