Question

Given that quadrilateral ABC D is a rectangle with AC = 3a and BD = 2x + 5, find the
value of x.

Answer 1

In a rectangle, the diagonals are equal in length. Given the lengths of the diagonals AC and BD, we can set them equal to each other:

\[
AC = BD
\]

Given:
\[
AC = 3a \quad \text{and} \quad BD = 2x + 5
\]

Setting them equal:

\[
3a = 2x + 5
\]

To find the value of \( x \), we need a specific value for \( a \). However, we can still manipulate the equation to express \( x \) in terms of \( a \):

1. Rearrange the equation to isolate \( x \):

\[
2x = 3a - 5
\]

2. Divide both sides by 2:

\[
x = \frac{3a - 5}{2}
\]

If you have a specific value for \( a \), you can substitute it into the equation to find \( x \). Otherwise, \( x \) is expressed in terms of \( a \) as shown above. Without further information about \( a \), we cannot provide a numerical answer for \( x \).