Question
ΔABP ~ ΔDEF and A(ΔABP) : A(ΔDEF) = 144:81, then AB : DE = ?
✓
Answer
$\frac{ A (\Delta ABP )}{ A (\Delta DEF )}=\frac{144}{81} \quad \ldots . .$. (i) $[$ Given $]$
$\frac{ A (\triangle ABP )}{ A (\triangle DEF )}=\frac{ AB ^2}{ DE ^2} \quad \ldots \ldots . .$. (ii) $[$ Theorem of areas of similar triangles $]$
$\therefore \frac{ AB ^2}{ DE ^2}=\frac{144}{81} \quad \ldots \ldots . . .[$ From (i) and (ii)]
$\therefore \frac{ AB }{ DE }=\frac{12}{9}$ or $\frac{4}{3} \quad \ldots \ldots .$. Taking square root of both sides]
$\frac{ A (\triangle ABP )}{ A (\triangle DEF )}=\frac{ AB ^2}{ DE ^2} \quad \ldots \ldots . .$. (ii) $[$ Theorem of areas of similar triangles $]$
$\therefore \frac{ AB ^2}{ DE ^2}=\frac{144}{81} \quad \ldots \ldots . . .[$ From (i) and (ii)]
$\therefore \frac{ AB }{ DE }=\frac{12}{9}$ or $\frac{4}{3} \quad \ldots \ldots .$. Taking square root of both sides]
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