Question

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

Answer 1

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.