Question

Use the image to answer the question.

A rectangle upper A upper B upper C upper D has diagonals upper A upper C and upper B upper D. The diagonals insect at upper O, in the center. Diagonal upper A upper C is labeled 7 x. Diagonal upper B upper C is labeled 2 x plus 5.

Given that quadrilateral ABCD
is a rectangle with AC=7x
and BD=2x+5
, find the value of x
. then find the value of AC
and BD
.

(1 point)
x =


AC=


BD=


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Answer 1

Diagonals of a rectangle are equal, so 7x = 2x + 5.
Solve: 5x = 5 → x = 1.

AC = 7x = 7(1) = 7
BD = 2x + 5 = 2(1) + 5 = 7