Question

In quadratic ABCD, AC = x + 2 and BD = 2x - 7. For what value of x is ABCD a rectangle?

a) x = 5
b) x = 7
c) x = 9
d) x = 11

Answer 1

To find the value of x that makes quadrilateral ABCD a rectangle, we set the diagonals equal to each other (AC = BD) and solve the equation x + 2 = 2x - 7. The solution to this equation is x = 9.

Step-by-step explanation:

The student asked, "In quadrilateral ABCD, AC = x + 2 and BD = 2x - 7. For what value of x is ABCD a rectangle?" In a rectangle, the diagonals are equal. Therefore, to find the value of x that makes ABCD a rectangle, we set AC equal to BD.

Therefore, the equation is x + 2 = 2x - 7. Solving for x:

1. Subtract x from both sides: x + 2 - x = 2x - 7 - x, which simplifies to 2 = x - 7.
2. Add 7 to both sides: 2 + 7 = x - 7 + 7, which simplifies to 9 = x.

Therefore, the value of x for which ABCD is a rectangle is x = 9.