Question

The sides of a triangle are x , x + 1 and 2 x -1. It’s area is x √10 square units. Find the value of x. ​

Answer 1

Solution :

$a = x \\ \\ b = x + 1 \\ \\ c = 2x - 1 \\ \\ s = \dfrac{a + b + c}{2} \\ \\ = \dfrac{x + (x + 1) + (2x - 1)}{2} = 2x \\ \\ => Area \: = \sqrt{s(s - 1)(s - b)(s - c)} \\ \\ => \sqrt{2x(2x - 1)(2x - x+1)(2x - 2x - 1)} \\ \\ => \sqrt{2x(x)(x - 1)(1)} \\ \\ => x \sqrt{2(x - 1)} \\ \\ According \: to \: question \\ \\ Area = x\sqrt{10} \\ \\ \implies x\sqrt{2(x - 1)} = x \sqrt{10} \\ \\ \implies \: \sqrt{2(x - 1)} = \sqrt{10} \\ \\ \implies2(x - 1) = 10 \\ \\ \implies x - 1 = 5 \\ \\ \implies x = 6$