Answers

2015-06-01T17:36:29+08:00

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Hi so this is how you solve it:

We let the width of the swimming pool be x, this would make the length be x + 8 since it is 8m longer than the width.

So:
Area = length * width
105m² = (x+8)m*(x)m
105= (x+8)(x)
105= x² +8x
0 = x² + 8x - 105
 
Method 1: Guess and Check
We look for two numbers with a product of 105 and a difference of 8 so:
105 - 1 = 104 X
35 - 3 = 32 X
21 - 5 = 16 X
15 - 7 = 8 √

So,
0 = x² + 8x - 105
0 = (x-7)(x+15)
We equate each to zero (since one factor needs to be zero in order for the product to be zero)
If (x-7) = 0           If (x+15) = 0
x = 7                  x = -15
 We cannot have a negative length so the width is equal to 7m and the length is equal to 15m.

Method 2: Quadratic Formula
x² + 8x - 105.
x= -8 ± √(8²+420) = -8 ± √(64+420) = -8 ± √484 = -8 ± 22 = 7 or -15
              2                        2                   2              2 
So then again, a length cannot be negative so the width is equal to 7m and the length is equal to 15m.


0