volume_mute
Find the Unknown in △DEF ∼ △GHI
publish date: 2026/05/14 21:40:17.856628 UTC
volume_mute
In the figure, \(\triangle DEF \sim \triangle GHI\). Given \(DE = 4.5\), \(GH = 9\), and \(EF = 13.5\), find \(y = HI\).
Correct Answer
27
Explanation
Use the proportion of corresponding sides: \(\dfrac{DE}{GH} = \dfrac{EF}{HI}\)
\(\dfrac{4.5}{9} = \dfrac{13.5}{y}\)
Cross multiply: \(4.5y = 9 \times 13.5 = 121.5\) → \(y = 27\).
Reference
Mathematics for college students