The sides of a triangle are x, x+1,2x-1 and its area is x root 10. find the value of x

You can use Heron's formula to solve this problem.

, where A is the area; a,b,с are the sides;  s is the semiperimeter of the triangle


According to conditions:
a = x
b = x+1
с = 2x-1

Calculate the semiperimeter:


Now we can compose and solve the equation according to Heron's formula:


As a result, x = 6 is your answer.
 
I hope this helped.