Question

given rectangle klmn below, no = 48. if km = 2x + 4, solve for x.

Explanation:

Step1: Recall rectangle diagonals property

In a rectangle, diagonals are equal and bisect each other. So, diagonal \( KM = LN \) and \( NO=\frac{1}{2}LN \), which implies \( LN = 2\times NO \). Given \( NO = 48 \), then \( LN=2\times48 = 96 \). Also, \( KM = LN \) (diagonals of rectangle are equal), so \( KM = 96 \).

Step2: Solve for \( x \)

We know \( KM = 2x + 4 \) and \( KM = 96 \). So, set up the equation \( 2x + 4=96 \). Subtract 4 from both sides: \( 2x=96 - 4=92 \). Then divide both sides by 2: \( x=\frac{92}{2}=46 \).

Answer:

\( x = 46 \)