Question

The length of a rectangle is 4 inches less than twice its width. If the area of the rectangle is 70 square inches, what are its demensions

Answer 1

let
x-----------> the length side of rectangle
y----------> the width side of rectangle

we know that
70=x*y--------> x=70/y-----------> equation 1
x-4=2y--------> equation 2
substitute equation 1 in equation 2

[70/y]-4=2y--------> multiply by y------> 70-4y=2y²----> 2y²+4y-70=0

using a graph tool ----> to resolve the second order equation
see the attached figure

the solution is
y=5
x=70/y--------> x=70/5=14

the answer is
the dimensions are
length=14 in
width=5 in

Answer 2

By definition, the area of a rectangle is given by:
A = w * l
Where,
w: width
l: long
Substituting values we have:
70 = w * (2w-4)
Rewriting we have:
70 = 2w ^ 2-4w
2w ^ 2 - 4w - 70 = 0
Solving the polynomial we have:
w1 = -5
w2 = 7
We take the positive root because it is a dimension.
w = 7 inches
Then, the length will be:
l = 2w-4
l = 2 (7) -4
l = 14-4
l = 10 inches
Answer:
its demensions are:
w = 7 inches
l = 10 inches