In the figure, LQ intersects MP at point R, and LM is parallel to PQ. The lengths of MR and RP are 8 and 14 units, respectively. The area of LMR is 36 square units. What is the area of PQR, in square units?

In the figure, LQ intersects MP at point R, and LM is parallel to PQ. The lengths of MR... | SAT Area and volume Practice

Context: $\overline{LM} \parallel \overline{PQ}$ ; $MR = 8$ , $RP = 14$ ; area of $\triangle LMR = 36$ .

Answer: $\triangle LMR \sim \triangle PQR$ by AA. Scale factor $k = \dfrac{14}{8} = \dfrac{7}{4}$ . Area ratio $= k^2 = \dfrac{49}{16}$ . Area of $\triangle PQR = 36 \times \dfrac{49}{16} = \dfrac{441}{4}$ .

Why D: Areas of similar triangles scale as the square of the linear scale factor.

Traps: A ( $\dfrac{576}{49}$ ) uses the inverse ratio. B ( $\dfrac{144}{7}$ ) misapplies the ratio. C ( $63$ ) multiplies by $k$ instead of $k^2$ .

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SAT Area and volume practice question

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