Question

lmnp is a rectangle. find the value of x and the length of each diagonal. ln = 7x - 2 and mp = 3x + 3 x = \square (simplify your answer.)

Explanation:

Step1: Use property of rectangle diagonals

In a rectangle, the diagonals are equal. So \(LN = MP\).
Given \(LN = 7x - 2\) and \(MP=3x + 3\), we set up the equation \(7x-2=3x + 3\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(7x-3x-2=3x - 3x+ 3\), which simplifies to \(4x-2 = 3\).
Add \(2\) to both sides: \(4x-2 + 2=3 + 2\), so \(4x=5\).
Divide both sides by \(4\): \(x=\frac{5}{4}=1.25\).

Answer:

\(x = 1.25\)