Question

AB=AC and ∠A is right angle in ΔABC. If BC = √2 a, then find the area of the triangle. (a ∈ R, a > 0)

Answer 1

Dear Student,

Solution: Since given triangle is Right angle triangle

ATQ

AB = AC

Base = perpendicular

As BC = √2 a

it shows that AB =AC = a

Since from Pythagoras theorem BC = √(AB)²+ (AC)²

BC = √(a²+a²)

BC = √(2a²)

BC = a √2

So area is ar(Δ ABC ) = 1/2 X (AB) X (AC)

ar(Δ ABC ) = 1/2 (a)(a)

ar(Δ ABC ) = 1/2 a²

Hope it helps you.

Answer 2

It is given that ,

In triangle ABC ,

<A = 90° ,

AB = AC = x

**********************************
By Phythogoras Theorem :

In a right angled triangle , the Square of

length of the hypotenuse is equal to the

of the square of lengths of the other

two sides .

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BC² = AB² + AC²

( √2 a )² = x² + x²

( √2 a )² = 2x²

( √2 a )² = ( √2 x )²

√2 a = √2 x

a = x ---( 1 )

Now ,

Area of ∆ABC = ( base × altitude )/2

A = ( AB × AC )/2

A = ( x ² )/2

A = a²/2 [ from ( 1 ) ]

I hope this helps you ,

: )