Question

A rectangular swimming pool is to be built with an area of 1800 square feet. The owner wants 5- foot wide decks along the two sides and 10-foot wide decks at the two ends. Find the dimensions of the smallest piece of land on which the pool (including the decks) can be built satisfying these conditions.

Answer 1

Answer:  $y = 20\sqrt{15}feet$, $x = 10\sqrt{15}feet$

Step-by-step explanation:

given data:

area of the pool = 1800 square feet.

length along the deck = 5- foot

length of side along the deck = 10-foot

Solution:

dimension of  the pool = $x * y$

total area $A = (20+y)(10+x)$$...................eqn1$

since $xy = 3000$

$y = \frac{3000}{x}$$..............................eqn2$

insert eqn2 into eqn1

$A = (\frac{3000}{x} +20)(10+x)$

$A = \frac{3000(x+10)}{x^{2} } + \frac{3000}{x} +20$

$20 - \frac{30000}{x^{2} } = 0$

$x = 10\sqrt{15}$feet

to solve for y, $\frac{60000}{x^{3} }$

$y = 20\sqrt{15}$