SOLUTION: Please help trying to set up the problems but i keep getting stuck. This problem is not in the book. However she said change the numbers and it is a practice question from chapter

Question 206360: Please help trying to set up the problems but i keep getting stuck.
This problem is not in the book. However she said change the numbers and it is a practice question from chapter 8.
Problem #1:The product of two positive numbers is 16. Determine the numbers if the larger is 4 times the smaller.
Problem #2: the length of a rectangle is 3 feet longer than ist width. Find the dimensions of the rectangle if its area is 28 square feet.
Found 2 solutions by Alan3354, Earlsdon:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Problem #1:The product of two positive numbers is 16. Determine the numbers if the larger is 4 times the smaller.
--------
x*4x = 16
4x^2 = 16
x^2 = 4
x = 2, other = 8
x = -2, other = -8
------------------
Problem #2: the length of a rectangle is 3 feet longer than ist width. Find the dimensions of the rectangle if its area is 28 square feet.
w*(w+3) = 28
w^2 + 3w - 28 = 0
(w+7)*(w-4) = 0
w = 4
L = 7
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
#1. Let n be the smaller number, then 4n is the larger number.
Their product is 16, so...

Divide both sides by 4.
Take the square root of both sides.
and
#2. Start with the formula for the area of a rectangle of length = L and width = W.
Substitute and
Simplify.
Subtract 28 from both sides.
Factor this.
Apply the zero product rule.
or so that...
or Discard the negative solution as the width, W, can only be a positive value.

The length is 7 feet and the width is 4 feet.
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