Question

A rectangular pool measures 10m by 5m. A deck, of uniform width, is to be built all the way around the pool such that the total area of the pool and deck will be126m2 . Set up and solve a quadratic equation to determine the width of the deck.

Answer 1

Answer:

The width of the deck is 2m .

Step-by-step explanation:

Let the width of the pool be represented by w. As stated in the problem a deck of uniform width is to be built so the total width of the pool and deck will be w+w = 2w.

Now the total dimensions can be taken as

10m+ 2w and 5m + 2w of both the pool and deck.

Area = length * breadth

126m ²= (10m+ 2w) ( 5m + 2w )

126= 50 + 30 w+ 4w²

0= 50 -126+ 30 w+ 4w²

0 = 30 w+ 4w²- 76

Taking 2 as common

0= 2( 15 w+ 2w² - 38)

2w²+ 15 w - 38= 0

The above equation is the quadratic equation and can be solved as follows.

a= 2 , b= 15 and c= -38

b= -b±√b²- 4ac/2a

Putting the values

b= - 15±√15²- 4( 2)(-38)/2(2)

b= - 15± 23/4

b= - 38/4 or 8/4

b= 2 m

The width cannot be negative so we ignore the negative value

The width of the deck is 2m .

The can be checked by putting the value in the original equation.

126m ²= (10m+ 2w) ( 5m + 2w )

126m ²= (10m+ 2(2)) ( 5m + 2(2) )

126m ²= (10m+ 4) ( 5m + 4 )

126m ²= 14*9

126m ²= 126m ²