In the diagram above, \(\overline{MN} || \overline{KL}\), \(\overline{ML}\) and \(\overline{KN}\) intersect at X. |\(\overline{MN}\)| = 12cm, |\(\overline{MX}\)| = 10cm and |\(\overline{MN}\)| = 9cm. If the area of \(\triangle\) MXN is 16cm\(^2\), calculate the area of \(\triangle\) LXK

infinitehoaxx

8 months ago

Answer: 9 cm²

Solution:
Since MN ∥ KL, triangles ΔLXK and ΔMXN are similar (AA).
Corresponding side ratio = KL/MN = 9/12 = 3/4.
The ratio of areas of similar triangles equals the square of the side ratio:
Area(ΔLXK) / Area(ΔMXN) = (3/4)² = 9/16.
Given Area(ΔMXN) = 16 cm²
⇒ Area(ΔLXK) = Area(ΔMXN) * ( Area(ΔLXK) / Area(ΔMXN) ) = 16 × 9/16 = 9 cm².

(Notice |MX| = 10 cm isn’t needed.)