Question

IF SIDES OF A TRIANGLE ARE x,x+1,2x-1 and area of triangle is x underoot10

Answer 1

$let \: \: the \: \: sides \: \: be \\ a = x \\ b = x + 1 \\ c = 2x - 1 \\ s = \frac{a + b + c}{2} = 2x \\ area = \sqrt{s(s - a)(s - b)(s - c)} \\ \sqrt{2x \times x \times (x - 1) \times 1} = x \sqrt{10 } \\ 2 {x}^{2} (x - 1) = 10 {x}^{2} \\ x - 1 = 5 \\ x = 6 \\ \\ therefore \: \: the \: \: sides \: \: are \\ 6 \: \: \: \: \: \: 7 \: \: \: \: \: \: 11$