Question

what is the perimeter of rhombus lmno? 20 units 24 units 40 units 48 units

Explanation:

Step1: Use the property of a rhombus (all sides are equal)

In a rhombus \(LMNO\), \(LM = MN\). So, \(3x - 3=x + 7\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(3x-x-3=x - x+7\), which gives \(2x-3 = 7\).
Add \(3\) to both sides: \(2x-3 + 3=7 + 3\), so \(2x=10\).
Divide both sides by \(2\): \(x=\frac{10}{2}=5\).

Step3: Find the length of a side

Substitute \(x = 5\) into \(x + 7\) (or \(3x-3\)). Using \(x + 7\), we get \(5+7 = 10\) units.

Step4: Calculate the perimeter

The perimeter \(P\) of a rhombus is \(4\times\) side length. So \(P = 4\times10=40\) units.

Answer:

40 units