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.

(1 point)
x=

Answer 1

In a rectangle, the diagonals are equal in length. Therefore, we can set the lengths of the diagonals equal to each other:

\[
7x = 2x + 5
\]

Next, let's solve for \( x \).

1. Subtract \( 2x \) from both sides:

\[
7x - 2x = 5
\]

\[
5x = 5
\]

2. Divide both sides by 5:

\[
x = 1
\]

Thus, the value of \( x \) is:

\[
\boxed{1}
\]