Question

Use the image to answer the question.

A parallelogram with vertices upper A upper B upper C upper D.

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=6
x equals 6

x=4
x equals 4

x=3
x equals 3

x=8
x equals 8
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Answer 1

In a parallelogram the diagonals bisect each other, so AC = 48 gives AO = 24. If the diagonals are congruent then BD = AC = 48, so DO = 24. Solve 7x + 3 = 24 → 7x = 21 → x = 3.