Question

ABCD is a rectangle with dimension 36*90. If P is a point on one of the longer side BC with 2*PD=PA then what is the length of PB

Answer 1

let PB = y ,PC = z ,PD = x & PA = 2x
y + z = 90
z = 90 - y
from pythagoras theorem
x² = 36² + z²
(2x)² = 36² + y²
4*36² + 4z² = 36² + y²
put z = 90 - y , we get
y² - 240y + 12096 = 0
y² - 168y - 72y + 12096 = 0
y(y - 168) -72(y - 168) = 0
(y - 168)(y - 72) = 0
y = 168
y = 72
as longer side is 90 hence y = 168 is not possible
length of PB = 72