Question

ΔABC is a right triangle with AB=BC. If bisectors of ∠A meets BC at D and AD= 2√2 cm, then the perimeter of ΔABC is

Answer 1

Answer:

Step-by-step explanation:

In Δ , ABC right angled at A and AB = AC  

Hence ∠ A = ∠ B  

We know that Sum of angles of a triangle = 180º  

∠A+ ∠B+ ∠C=180º  

90º+∠B+∠B=180º  

2∠B=180º -90º  

2∠B=90º  

∠B=45º………………………………………..(i)  

ALSO , AD is the bisector of BAC  

So , ∠BAD = ∠CAD = 90º/2 = 45º …………………………….(ii)  

∠BAD = ∠ABC  

SO, AD = BD ………………………………(iii) .  

Similarly angle CAD = angle ACD  

So, AD = DC ………………………………..(iv)  

adding equation (iii) and (iv)  

We will get, AD + AD = BD+DC  

2AD = BC