Question

ABC is an isosceles triangle right angled at C. Prove that AB : AC = √2 : 1.

Answer 1

In an Isosceles Right Triangle,

The Sides other than the Hypotenuse are equal.

ie, AB = BC.

Therefore,

By Pythagoras Theorem,

${a}^{2} + {b}^{2} = {c}^{2}$

$2 {a}^{2} = {c}^{2}$

If we take a = 1,

$2 \times ( {1}^{2} ) = {c}^{2}$

$2 = {c}^{2}$

Therefore,

$c = \sqrt{2}$

Therefore,

a : c = 1 : √2
OR
AB : AC = 1 : √2

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