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A line PQ is drawn parallel to the side BC of ΔABC which cuts side AB at P and side AC at Q. If AB = 9.0 cm, CA = 6.0 cm and AQ = 4.2 cm, find the length of AP.

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Answer

Let AP = x cm.

From figure,

A line PQ is drawn parallel to the side BC of ΔABC which cuts side AB at P and side AC at Q. If AB = 9.0 cm, CA = 6.0 cm and AQ = 4.2 cm, find the length of AP. Similarity, Concise Mathematics Solutions ICSE Class 10.

PB = AB - AP = 9 - x cm.

QC = AC - AQ = 6 - 4.2 = 1.8 cm.

Given PQ || AB,

By basic proportionality theorem :

⇒APPB=AQQC⇒x9−x=4.21.8⇒1.8x=4.2(9−x)⇒1.8x=37.8−4.2x⇒1.8x+4.2x=37.8⇒6x=37.8⇒x=6.3 cm.\Rightarrow \dfrac{AP}{PB} = \dfrac{AQ}{QC} \\[1em] \Rightarrow \dfrac{x}{9 - x} = \dfrac{4.2}{1.8} \\[1em] \Rightarrow 1.8x = 4.2(9 - x) \\[1em] \Rightarrow 1.8x = 37.8 - 4.2x \\[1em] \Rightarrow 1.8x + 4.2x = 37.8 \\[1em] \Rightarrow 6x = 37.8 \\[1em] \Rightarrow x = 6.3 \text{ cm}.

Hence, AP = 6.3 cm.

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