Question

the sides of a triangle are x,x+1,2x-1 and its area is x√10what is the value of x full explain

Answer 1

The formula area of this type of triangle is
√[S(S-a)(S-b)(S-c)]

Where S=(a+b+c)/2
& a,b,c are the sides of the triangle

Let here a=x
b=(2x-1)
c=(x+1)
then S=(x+2x-1+x+1)/2=2x

Area of the triangle,
=√[2x(2x-x){2x-(2x-1)}{2x-(x+1)}]

According to the question,
the area of the triangle is x√10.

So √[2x(2x-x){2x-(2x-1)}{2x-(x+1)}]=x√10
=>√[(2x^2)(x-1)=x√10
squaring both the sides,
(2x^2)(x-1)=10x^2
=>x-1=(10x^2)/(2x^2)
=>x-1=5
=>x=5+1=6
Hence the required answer is 6.

Answer 2

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