Question

A rectangular pool is 30 feet wide and 40 feet long. It is surrounded on all four sides by a wooden deck that is x feet wide. The total area enclosed within the perimeter of the deck is 2000 square feet. What is the width of the deck?

Answer 1

Answer:

5 feet

Step-by-step explanation:

We are given that

Width of rectangular pool=b=30 feet

Length of rectangular pool=l=40 feet

Area of rectangle=$l\times b$

Using the formula

Area of rectangular pool=$30\times 40=1200ft^2$

Total area enclosed within the perimeter of  the deck=$2000ft^2$

Width of deck=x ft

Length of rectangular pool including wooden deck=40+2x ft

Width of  rectangular pool including wooden deck=30+2x ft

Area of rectangular pool including wooden deck=$(40+2x)(30+2x)$

According to question

$(40+2x)(30+2x)=2000$

$40(30)+2x(30)+40(2x)+2x(2x)=2000$

$1200+60x+80x+4x^2=2000$

$140x+4x^2=2000-1200=800$

$4x^2+140x-800=0$

$x^2+35x-200=0$ (Dividing by 4 on both sides)

$x^2+40x-5x-200=0$

$x(x+40)-5(x+40)=0$

$(x+40)(x-5)=0$

$x+40=0$

$x=-40$

It is not possible because width cannot be negative it is always natural number.

$x-5=0\implies x=5$

Hence, the width of the deck=5 ft