Question

choose the correct answer.
the length of a rectangular pool is 6 feet more than its width w. the area of the pool is 49 square feet. which equation could be used to find the area of the pool?

a. $w^2 + 6w + 49 = 0$

c. $w^2 - 6w + 49 = 0$

b. $w^2 - 6w - 49 = 0$

d. $w^2 + 6w - 49 = 0$

Explanation:

Step1: Define length in terms of width

The width of the pool is \( w \). The length is 6 feet more than the width, so length \( l = w + 6 \).

Step2: Recall the area formula for a rectangle

The area \( A \) of a rectangle is given by \( A = l \times w \). We know the area \( A = 49 \) square feet. Substitute \( l = w + 6 \) and \( A = 49 \) into the formula:
\( 49=(w + 6)\times w \)

Step3: Expand and rearrange the equation

Expand the right - hand side: \( 49 = w^{2}+6w \)
Then, rearrange the equation to the standard quadratic form \( ax^{2}+bx + c = 0 \) by subtracting 49 from both sides:
\( w^{2}+6w-49 = 0 \)

Answer:

d. \( w^{2}+6w - 49 = 0 \)