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In the figure, `PS=3`, `SQ=6`, `QR=5`, `PT=x` and `TR=y`. Give any two pairs of values of `x` and `y` such that line `ST||` side `QR`. |
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Answer» In `DeltaPQR`, line `ST||` side `QR` ………..(Given) `:.` by basic proportionally theorem, `(PS)/(SQ)=(PT)/(TR)` `:.(3)/(6)=(x)/(y)` `:.(1)/(2)=(x)/(y)` `:.y=2x` Consider `x=2`, then `y=2xx2=4` `:.` When `x=2` , then `y=4` is one possibility Consider `x=2.5`, then `y=2xx2.5=5` `:.` When `x=2.5`, then `y=5` is the other possibility Note : while selecting the values of `x` and `y` the student needs to be careful as the sum of the lengths of two sides of a triangle is greater than lengths of the third side. `:.x=` and `y=2` cannot be possible though it satisfies the equation `y=2x`. |
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