Question

the length of a rectangular room is 6 units greater than its width. write an equation expressing the rectangular room’s area, a, as a function of w.
a ( a = 2w + 6 )
b ( a = 4w + 12 )
c ( a = w^2 + 6w )
d ( a = w^2 + 12w )
e ( a = 2w^2 + 12w )

Explanation:

Step1: Recall area formula for rectangle

The area \( A \) of a rectangle is given by the formula \( A=\text{length} \times \text{width} \).

Step2: Identify length and width

From the problem, the width is \( w \), and the length is \( w + 6 \) (since length is 6 units greater than width).

Step3: Substitute into area formula

Substitute length \( l=w + 6 \) and width \( w \) into the area formula: \( A=w\times(w + 6) \).

Step4: Expand the expression

Using the distributive property (FOIL method), \( w\times(w + 6)=w^{2}+6w \).

Answer:

C. \( A = w^{2}+6w \)