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.

Answer 1

`"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.