The diagram shows a trapezium , pqrstuv that formed from the combination of two similar rectangles and a rightangled triangle.
given pt , qr and rs are (2x+5y)cm , 3y cm and (y-3/
2x)cm respectively. calculate the lenght of pq in terms of x and y .

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) ] .

.

c

-by-step explanation:

it would be c