In figure below, $Δ\ ACB\ ∼\ Δ\ APQ$. If $BC\ =\ 8\ cm$, $PQ\ =\ 4\ cm$, $BA\ =\ 6.5\ cm$ and $AP\ =\ 2.8\ cm$, find $CA$ and $AQ$.
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Given:
In the given figure $Δ\ ACB\ ∼\ Δ\ APQ$.
$BC\ =\ 8\ cm$, $PQ\ =\ 4\ cm$, $BA\ =\ 6.5\ cm$ and $AP\ =\ 2.8\ cm$.
To do:
We have to find the value of $CA$ and $AQ$.
Solution:
$Δ\ ACB\ ∼\ Δ\ APQ$ (given)
Therefore,
$\frac{BA}{AQ} = \frac{CA}{AP} = \frac{BC}{PQ}$ (Corresponding parts of similar triangles are proportional)
$\frac{6.5}{AQ} = \frac{8}{4}$
$AQ = \frac{6.5 \times 4}{8}$
$AQ = 3.25\ cm$
And,
$\frac{CA}{AP} = \frac{BC}{PQ}$
$\frac{CA}{2.8} = \frac{8}{4}$
$CA = 2.8 \times 2$
$CA = 5.6\ cm$
Hence, the values of $CA$ and $AQ$ are $5.6\ cm$ and $3.25\ cm$ respectively.
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