Question

A pool company offers a pool with dimensions x and 2x. They also include a 3 foot deck around the entire pool.

1. Write an equation to represent the area of the pool and deck combined.

2. If someone wants a 10ft wide pool (x = 10) how many square feet must they have available in their back yard?

Answer 1

#1

• New dimensions=x+3 and 2x+3ft

So

Area:-

• Length ×Breadth
• (x+3)(2x+3)
• x(2x+3)+3(2x+3)
• 2x^2+3x+6x+9
• 2x^2+9x+9ft^2

#2

Put x=10

• 2(10)^2+9(10)+9
• 2(100)+90+9
• 200+99
• 299ft^2

Answer 2

1) area = (x + 3)(2x + 3) ft²

2) 299 ft²

Explanation:

Question 1

Area of a rectangle = width x length

Given:

• width = x + 3
• length = 2x + 3

⇒ area = (x + 3)(2x + 3) ft²

Question 2

If x = 10:

⇒ area = (10 + 3)(2(10) + 3)

= 13 · 23

= 299 ft²