Given:
ABCD is isosceles trapezoid.
AC=3x-4 and BD=x+8 are the diagonals of the given trapezoid.
Required:
We need to find the value of x and the length of AC.
Explanation:
Recall that the diagonals of an isosceles trapezoid have the same length
[tex]AC=BD[/tex]
Substitute AC=3x-4 and BD=x+8 in the equation to find the value of x.
[tex]3x-4=x+8[/tex]
Add 4 to both sides of the equation.
[tex]3x-4+4=x+8+4[/tex][tex]3x=x+12[/tex]
Subtract x from both sides of the equation.
[tex]3x-x=x+12-x[/tex][tex]2z=12[/tex]
Divide both sides of the equation by 2.
[tex]\frac{2x}{2}=\frac{12}{2}[/tex][tex]x=6[/tex]
We get x =6 and substitute x =6 in the equation AC=3x-4 to find the length of AC.
[tex]AC=3(6)-4[/tex][tex]AC=14units[/tex]
Final answer:
[tex]x=6[/tex][tex]AC=14units[/tex]
