Question

the length of the rectangle above is 5 inches longer than the used to represent the area of the rectangle?
a. $5x^{2}$
b. $6x$
c. $x^{2}+5$
d. $x^{2}+5x$

Explanation:

Step1: Let width be \(x\)

Assume the width of the rectangle is \(x\) inches.

Step2: Find length

Since the length of the rectangle is 5 inches longer than the width, the length is \((x + 5)\) inches.

Step3: Calculate area

The area \(A\) of a rectangle is given by \(A=\text{length}\times\text{width}\), so \(A=x(x + 5)\).
Using the distributive property \(a(b + c)=ab+ac\), we have \(A=x\times x+x\times5=x^{2}+5x\).

Answer:

D. \(x^{2}+5x\)