Answer:
PQ = √ [ 4(x + y)^2 + (y - 3)^2 )/ x^2 ]
Step-by-step explanation:
I am assuming that the 2 rectangles are congruent so RS = ST.
UT = QR = 3y cm.
PU = PT - UT
= 2x + 5y - 3y
= 2x + 2y.
RT = = 2 * RS = 2*(y - 3) / 2x = (y - 3)/x ( as the rectangles are congruent).
Thus QU = (y - 3)/x ( as QU = RT).
By Pythagoras:
PQ^2 = PU^2 + QU^2
= (2x + 2y)^2 + (y - 3)^2 / x^2
= 4(x + y)^2 + (y - 3)^2 / x^2
PQ = √ [4(x + y)^2 + (y - 3)^2 / x^2) ] .
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