Question

Draw segment AB of length root65 without using Pythagoras theorem

Answer 1

Segment AB of length

Step-by-step explanation:

In triangle ABC ,(From figure.1)

$\angleABC =90^{o}\\\\Seg\,BD\perp \,hypotenuse\,AC$

$\therefore \triangle ABC\sim \triangle ADB$     [Theorem on similarity of right angle triangle]  

$\therefore\frac{AB}{AD}=\frac{AC}{AB}\,\,\,\, [C.S.S.]\\\\\therefore\,AB^{2}=AD\times AC\\\\\therefore\,AB^{2}=5\times 13\\\\\therefore\,AB^{2}=65\\\\\therefore\,AB=\sqrt{65}$

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