Question

A diagonal connects vertex upper A in the top left to vertex upper C in the bottom right. Another diagonal line connects vertex upper B in the lower left to vertex upper D in the top right. These diagonals intersect at a point upper O, in the middle of the parallelogram.


Because congruent diagonals prove that a parallelogram is a rectangle, what value of x proves that parallelogram ABCD
is a rectangle if AC=48
and DO=7x+3
?

(1 point)
Responses

x=3

x equals 3

x=4

x equals 4

x=8

x equals 8

x=6

Answer 1

Diagonals of a parallelogram bisect each other, so BD = 2·DO = 2(7x+3). For the parallelogram to be a rectangle BD = AC = 48:
2(7x+3) = 48 → 14x+6 = 48 → 14x = 42 → x = 3.

Answer: x = 3.