Question

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 .

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Answer 1

PQ = √ [ 4(x + y)^2 + (y - 3)^2 )/ x^2 ]

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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