Question

a rectangle has a length of 7xy and a width of 12xy. what is the area of the rectangle? 19xy 84x²y² 19x²y² 84xy

Explanation:

Step1: Recall the formula for the area of a rectangle

The area formula for a rectangle is \(A = \text{length}\times\text{width}\). Here, length \(l = 7xy\) and width \(w=12xy\).

Step2: Substitute the values into the formula

\(A=(7xy)\times(12xy)\).

Step3: Use the rules of multiplication for algebraic expressions

When multiplying \(7xy\times12xy\), we use the rule \(a\times b\times c\times d=(a\times c)\times(b\times d)\). So, \((7\times12)\times(x\times x)\times(y\times y)\).
Since \(7\times12 = 84\), \(x\times x=x^{2}\), and \(y\times y = y^{2}\), then \(A = 84x^{2}y^{2}\).

Answer:

\(84x^{2}y^{2}\) (the second option)