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Question

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are diagonals of ABCD. What value of x makes ABCD a rectangle if AC = x + 29 and BD = 4x - 1.

(1 point)
Responses

x = 15
x = 15

x = 10
x = 10

x = 6
x = 6

Answer 1

In a rectangle, the diagonals are equal in length. Therefore, we can set the lengths of the diagonals \( AC \) and \( BD \) equal to each other:

\[ x + 29 = 4x - 1 \]

To solve for \( x \), first, let's rearrange the equation:

1. Subtract \( x \) from both sides: \[ 29 = 4x - x - 1 \] Which simplifies to: \[ 29 = 3x - 1 \]

2. Next, add \( 1 \) to both sides: \[ 29 + 1 = 3x \] Thus: \[ 30 = 3x \]

3. Finally, divide by \( 3 \): \[ x = 10 \]

So, the value of \( x \) that makes \( ABCD \) a rectangle is \( x = 10 \).