Question

1. the area of the surface of the swimming pool is 210 square feet. what is the length d of the deep end (in feet)?

Explanation:

Step1: Identify the shape and formula

The swimming pool surface is a rectangle? No, wait, looking at the diagram, it's a composite of two rectangles? Wait, no, actually, the total surface area is the area of a rectangle with width 10 ft and length (d + 9) ft? Wait, no, wait the diagram: the deep end and shallow end, the width is 10 ft (vertical side), and the total length is d + 9 ft. So the area of a rectangle is length × width. So the formula for the area \( A \) is \( A = 10 \times (d + 9) \)? Wait, no, wait the area is given as 210 square feet. Wait, let's check again. Wait, the width is 10 ft (the vertical side), and the horizontal length is d (deep end) plus 9 ft (shallow end). So the area of the rectangle (since it's a rectangular pool surface) is \( \text{length} \times \text{width} \), where length is \( d + 9 \) and width is 10. So \( A = 10(d + 9) \). We know \( A = 210 \), so we can set up the equation.

Wait, no, maybe I misread. Wait, the diagram: the deep end has length d, shallow end has length 9 ft, and the width (the side perpendicular to d and 9) is 10 ft. So the total area is the area of the deep end rectangle plus the area of the shallow end rectangle? Wait, no, actually, the entire surface is a single rectangle with length \( d + 9 \) and width 10. So area \( A = 10 \times (d + 9) \). Let's confirm:

Given \( A = 210 \), so:

Step2: Set up the equation

\( 10(d + 9) = 210 \)

Step3: Solve for d

First, divide both sides by 10:

\( d + 9 = \frac{210}{10} = 21 \)

Then, subtract 9 from both sides:

\( d = 21 - 9 = 12 \)

Answer:

12