Question

ΔABC is an isosceles triangle in which ∠C=90∘.If AC=6 cm,then AB=_____

Answer 1

Hello,

Given :-
Triangle ABC is a isosceles triangle and Angle C is 90 degrees.
Also,
AC = 6 cm

Now,
Please refer the above attachment for the figure.


Now,
AC =BC
(triangle is isosceles)
So,
BC = 6 cm

Also,
The triangle is a right triangle

applying Pythagoras theorem to obtain the value of AB

${ab}^{2} = {bc}^{2} + {ac}^{2}$
So now

$ab = \sqrt{ {bc}^{2} + {ac}^{2} }$
So
Putting the values
$ab = \sqrt{ {6}^{2} + {6}^{2} } \\ ab = \sqrt{36 + 36} = \sqrt{72} \\ ab = 6 \sqrt{2} \: \: cm$
So,

The value of AB is 6root2 cm.

Hope this will be helping you ✌️

Answer 2

Given :-

Triangle ABC is a isosceles triangle and Angle C is 90 degrees.

Also,

AC = 6 cm

Now,

Please refer the above attachment for the figure.

Now,

AC =BC

(triangle is isosceles)

So,

BC = 6 cm

Also,

The triangle is a right triangle

applying Pythagoras theorem to obtain the value of AB

So now

So

Putting the values

So,

The value of AB is 6root2 cm.