lines AC and BD are diagonals of ABCD. what values of x make ABCD a rectangle if AC =x+7 and BD = 3x-5?
x=6
x=8
x=15
x=13
To determine the values of x that make ABCD a rectangle, we need to use the properties of rectangles. One property of a rectangle is that its diagonals are congruent. Therefore, we can set up an equation using the given information:
AC = BD
(x+7) = (3x-5)
Now, solve for x:
x+7 = 3x-5
7+5 = 3x-x
12 = 2x
x = 6
So, the value of x that makes ABCD a rectangle is x = 6.
Therefore, the correct answer is x = 6.