[tex]7x + 12 = 9x - 6[/tex]
[tex]7x + 12 - 7x = 9x - 6 - 7x[/tex]
[tex]12 = 2x - 6[/tex]
[tex]12 - 6 = 2x -6 - 6[/tex]
[tex]6 = 2x - 12[/tex]
[tex]6 + 12 = 2x[/tex]
[tex]18 = 2x[/tex]
[tex]18 \div 2 = x[/tex]
[tex]9 = \bold{ x}[/tex]
In pythagoras, c is the hypotenuse. That is AC. Where a is AB and b is BC.
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
[tex] {(6 x + 5)}^{2} = {(7x + 12)}^{2} + {BC}^{2} [/tex]
[tex] {((6 \times 9) + 5)}^{2} = {((7 \times 9)}^{2} + 12)^{2} +{BC}^{2} [/tex]
[tex] {(54 + 5)}^{2} = {(63 + 12)}^{2} + {BC}^{2} [/tex]
[tex] {59}^{2} = {75}^{2} + {BC}^{2} [/tex]
[tex]3481 = 5625 + {BC}^{2} [/tex]
[tex]3481 - 5625 = {BC}^{2} [/tex]
[tex] - 2144 = {BC}^{2} [/tex]
[tex] \sqrt{ - 2144} = BC[/tex]
