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Question
PQRS is a square with each side 6cm. T is a point on QR such that the `"area of ΔPQT"/"area of trapezium PTRS" = (1)/(3)` Find the length of TR.
Solution
`"Area of ΔPQT"/"Area of trapezium PTRS" = (1)/(3)`
⇒ `((1)/(2) xx "PQ" xx "QT")/((1)/(2) xx ("TR" + "SP") xx "RS") = (1)/(3)`
⇒ `("PQ" xx ("QR" - "TR"))/(("TR" + "SP") xx "RS") = (1)/(3)`
⇒ `(6 xx (6 - "TR"))/(("TR" + 6) xx 6) = (1)/(3)`
⇒ `(36 - 6"TR")/("TR" + 6)` = 2
⇒ 36 - 6TR = 2TR + 12
⇒ 8TR = 24
⇒ TR = 3cm.
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