$\triangle A B C$ is an isosceles triangle with $\angle$ C=90* and $ A C=5 cm. Then, A B=?

a) 25cm

b) 5cm

c) 10cm

d) $5 \sqrt{2} $cm

Given: ABC is an isosceles triangle, right-angled at C.

To Find: AB 

Solution:

Angle C = 90°

so, AB  = hypotenuse,

AC = BC

In isosceles triangle two sides are equal.

AC  = 5   ;  BC  =  5 ; AB = ?

Since its a right angled triangle, apply Pythagoras theorem,

$AB^2   =  AC^2   +  BC^2$     

$AB^2   =   5^2   +  5^2$   

$AB^2   =  25 + 25$

$AB^2   =  50$

$AB  =  √50$

$AB  =  √2 \times 5 \times 5$

So, the value of AB  =  5√2 

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Updated on: 10-Oct-2022

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