Question

lmnp is a rectangle. find the value of x and the length of each diagonal. ln = 3x + 3 and mp = 9x - 9

Explanation:

Step1: Recall rectangle diagonal property

In a rectangle, diagonals are equal. So \( LN = MP \).

Step2: Set up equation

Given \( LN = 3x + 3 \) and \( MP = 9x - 9 \), set them equal: \( 3x + 3 = 9x - 9 \).

Step3: Solve for x

Subtract \( 3x \) from both sides: \( 3 = 6x - 9 \).
Add 9 to both sides: \( 12 = 6x \).
Divide by 6: \( x = 2 \).

Answer:

\( x = 2 \)