Answer:the length is 8.7 inches. The width is 5.7 inches
Step-by-step explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
The width of a rectangle is 3 inches less than the length. This means that
L = W + 3
The area of a rectangle is expressed as L×W
The area is 50 square inches. This means that
LW = 50 - - - - - - - - - - 1
Substituting L = W + 3 into equation 1, it becomes
(W + 3)W = 50
W^2 + 3W - 50 = 0
We would apply the general formula for quadratic equations,
x = [ - b ± √(b^2 - 4ac)]/2a
a = 1
b = 3
c = - 50
Therefore,
w = [- 3 ± √(3^2 - 4×1×-50)]/2×1
w = [- 3 ± √(9 + 200)]/2
w = (- 3 ± √209)/2
w = (-3+14.4568)/2 or (-3-14.4568)/2
w = 5.7 or w = -8.7
Since the width cannot be negative, the width would be 5.7 inches.
Substituting w = 5.7 into L = W + 3,
L = 5.7 + 3 = 8.7 inches
