Question : In $\triangle A B C, P$ and $Q$ are points on $AB$ and $BC$, respectively, such that $PQ\parallel AC$. Given that $AB=26, PQ=7$ and $AC=10$, then find the value of $AP$.
Option 1: 7.1
Option 2: 7.8
Option 3: 18.2
Option 4: 16.4
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Correct Answer: 7.8
Solution :
In $\triangle A B C, PQ\parallel AC$.
Also, $A B=26, P Q=7$ and $A C=10$
Since $PQ\parallel AC$,
So, $\triangle ABC \sim \triangle PBQ$
⇒ $\frac{AB}{BP}=\frac{AC}{PQ}$
⇒ $\frac{26}{BP}=\frac{10}{7}$
⇒ $BP = 26\times 0.7$
⇒ $BP=18.2$
Now, $AB=BP+PA$
⇒ $26=18.2+AP$
⇒ $AP=26-18.2$
⇒ $AP=7.8$
Hence, the correct answer is 7.8.
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