What is the ratio of the area of triangle PQS | vedclass

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(C) The coordinates of $P$ and $Q$ are $(1, 2\sqrt{2})$ and $(1, -2\sqrt{2})$.The length of the base $PQ$ is $|2\sqrt{2} - (-2\sqrt{2})| = 4\sqrt{2}$.

Vedclass · Accepted Answer

$1 : 4$

Vedclass · Answer

(C) The coordinates of $P$ and $Q$ are $(1, 2\sqrt{2})$ and $(1, -2\sqrt{2})$.The length of the base $PQ$ is $|2\sqrt{2} - (-2\sqrt{2})| = 4\sqrt{2}$.Assuming the vertices $R$ and $S$ have $x$-coordinates such that the heights are $8$ and $2$ respectively:Area of $	riangle PQR = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes 4\sqrt{2} 	imes 8 = 16\sqrt{2}$.Area of $	riangle PQS = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes 4\sqrt{2} 	imes 2 = 4\sqrt{2}$.The ratio of the area of $	riangle PQS$ to the area of $	riangle PQR$ is $\frac{4\sqrt{2}}{16\sqrt{2}} = \frac{1}{4}$,which is $1 : 4$.

What is the ratio of the area of $\triangle PQS$ to the area of $\triangle PQR$?

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