Question

In a right angles triangle ABC, If ΔB=90 , BC = 3 CM ,AC = 5 CM then find the length of AB
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Answer 1

$\underline{ \red{Given:}}</h3><h3>$

• ∠B = 90°
• BC = 3cm
• AC = 5cm

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$\underline{ \red{To \: find:}}$

• length(AB)

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∴ Sides AB and BC are non-hypotenuse sides of the the right angled triangle and side AC is the hypotenuse of it.

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$∴ \: By \: pythagoras \: theorem, \\ \\ (Hypotenuse)^{2} = (Side) ^{2} + (Side)^{2} \\ \\ = > {(AC)}^{2} = {(AB)}^{2} + {(BC)}^{2} \\ \\ = > {(5)}^{2} = {(AB)}^{2} + {(3)}^{2} \\ \\ = > 25 = {(AB)}^{2} + 9 \\ \\ = > {(AB)}^{2} = (25 - 9 )\\ \\ = > {(AB)}^{2} = 16 \\ \\ = > AB= \sqrt{16} \\ \\ = > \green {\boxed{AB = 4\: cm}}$

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∴ The length of the side AB is 4cm.