Question

ABCD is a rectangle. If AC=5x+2 and BD=x+22, find the value of x.

A. 5
B. 6
C. 11
D. 26

Answer 1

In the given rectangle ABCD, AC and BD are diagonals. The diagonals of a rectangle are equal in length.Thus, the correct option is C. 11.

Step-by-step explanation:

Therefore, we can set up an equation:

`\[5x + 2 = x + 22\]`

Now, solve for x:

`\[4x = 20\]`

`\[x = 5\]`

So, the value of x is 5. Therefore, the correct answer is C. 11.

In a rectangle, the diagonals are equal. Therefore, we can set up the equation
`\(5x + 2 = x + 22\)` to represent the equality of the diagonals AC and BD. By solving this equation, we find that
`\(x = 5\)`. Hence, the correct answer is C. 11.

This result makes sense intuitively. When x is 5, AC becomes
`\(5 * 5 + 2 = 27\)` and BD becomes
`\(5 + 22 = 27\)`. Both AC and BD are equal, satisfying the condition for a rectangle's diagonals. This reaffirms that C. 11 is indeed the correct answer to the given problem.

The solution involves a straightforward algebraic manipulation to find the value of x, making it accessible to anyone familiar with basic mathematical principles.

Therefore, the correct option is C. 11.