Question

In a right-angled triangle ABC , AB=AC . Then a:b:c _______ .​

Answer 1

Answer: Step-by-step explanation:

let AC = x

then BC = 2–√x

as AD and DB will be in ratio of AC and BC by angle bisector theorem

so let AD = y and  so DB = 2–√y

but AD + DB = AB  = AC

so y+2–√y = x

   y(2–√ + 1) = x

 so y = x2–√+1

  on rationalising the denominator it results in

    y = (2–√ - 1) x

add x on both sides

    y + x=  (2–√ - 1) x + x

    AD + AC = (2–√ - 1 + 1)  x

    AD + AC = (2–√)  x

   so AC + AD = BC

Step-by-step explanation:

Answer 2

Given,

Right angled triangle ABC and

AB = AC

Find a : b : c

SOLUTION :-

from the figure, Let's consider

AB = x

such that, AC = x

now, finding BC :

by using Pythagoras theorem,

$\bf BC = \sqrt{AB {}^{2} + AC {}^{2} }$

$\rm⇢ \: \: BC = \sqrt{ {x}^{2} + {x}^{2} }$

$\rm⇢ \: \: BC = \sqrt{2} \cdot x$

now, finding ratio

AB : AC : BC

= x : x : √2.x

= 1 : 1 : √2

FINAL ANSWER :-

The required ratio is 1 : 1 : √2 .