Question

The area of a triangle is x√10.
Find the value of x if the sides of the triangle are x , x+1 , 2x-1 .​

Answer 1

Answer:

x=6

see the attachment

Answer 2

$\huge\mathbb\pink{Heya \:mate \:!!}$

Given :

The sides of triangle are x, x+1, and 2x-1

The area of triangle is x√10

To find :

The value of x

Solution :

Semi- perimeter = $\dfrac{x+x+1+2x-1}{2}$

⇒s = $\dfrac{4x}{2}$

⇒ s = 2x

Area of Δ by Heron's Formula :

⇒$a = \sqrt{s(s - a)(s - b)(s - c)}$

This implies :

$x \sqrt{10} = \sqrt{2x(2x - x)(2x - x)(2x-2x + 1)}$

⇒$x \sqrt{10} = \sqrt{2x \times x \times (x - 1)}$

⇒$x \sqrt{10} = \sqrt{2 {x}^{2} \times (x - 1) }$

⇒$x \sqrt{10} = x \sqrt{2(x - 1)}$

⇒$\sqrt{10} = \sqrt{2(x - 1)}$

⇒$10 = 2(x - 1)$

⇒$2x - 2 = 10$

⇒$2x = 12$

$\boxed{x\:=\:6}$