Question

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

Answer 1

2s=x+x+1+2x-1=4x
s=2 x
\[area~of ~\triangle=\sqrt{s \left( s-a \right)\left( s-b \right)\left( s-c \right)}\]
\[=\sqrt{2x \left( 2 x-x \right)\left\{ 2x-\left( x+1 \right) \right\}\left\{ 2 x-\left( 2x-1 \right) \right\}}\]
\[=\sqrt{2x \left( x \right)\left( x-1 \right)\left( 1 \right)}=\sqrt{2 x^2\left( x-1 \right)}=x \sqrt{2\left( x-1 \right)}\]
\[hence~x \sqrt{2\left( x-1 \right)}=x \sqrt{10}\]
\[\sqrt{2\left( x-1 \right)}=\sqrt{10}\]
x=?