Question

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

Explanation:

Step1: Identify the shape and formula

The swimming pool's surface is a rectangle (composed of deep end and shallow end). The area of a rectangle is \( A = \text{length} \times \text{width} \). The total length of the pool is \( d + 9 \) feet, and the width is 10 feet. The area \( A = 210 \) square feet. So the formula is \( 10\times(d + 9)=210 \).

Step2: Solve for \( d \)

First, divide both sides of the equation by 10:
\( \frac{10\times(d + 9)}{10}=\frac{210}{10} \)
Simplify: \( d + 9 = 21 \)

Then, subtract 9 from both sides:
\( d + 9 - 9 = 21 - 9 \)
Simplify: \( d = 12 \)

Answer:

The length of the deep end is 12 feet.