The width of a rectangle is 3ft less than the length, the area is 4ft^2 find the length and width
a=lw
w=l-3
therefore
a=(l-3)l
and a=4
therefore
4=l^2-3l
l=4(guess&check)
w=l-3
w=4-3
w=1
L=-2
because...
a=lw
4=(1-3)L
4=-2L
divide both sides by -2
-2=L
the length is l= -2
because area does equals length*width
which would be 4=(1-3)L
4=2L then you will have to divide both sides bby the negative 2
-2=L
To find the length and width of a rectangle given the information about the width being 3 feet less than the length and the area being 4 square feet, we can set up equations and solve for the variables.
Let L be the length of the rectangle.
Since the width is 3 feet less than the length, we can express the width as L - 3.
The area of a rectangle is calculated by multiplying its length by its width. Therefore, we have the equation:
Length × Width = Area
Substituting the values given, we get:
L × (L - 3) = 4
Expanding the equation:
L^2 - 3L = 4
Rearranging the equation to set it equal to zero:
L^2 - 3L - 4 = 0
Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, let's solve it by factoring.
Factoring the quadratic equation:
(L - 4)(L + 1) = 0
Setting each factor equal to zero and solving for L:
L - 4 = 0 or L + 1 = 0
L = 4 or L = -1
Since the length cannot be negative, we discard L = -1.
Therefore, the length of the rectangle is L = 4 feet.
To find the width, substitute the value of the length into the expression for the width:
Width = L - 3 = 4 - 3 = 1 foot
Thus, the length of the rectangle is 4 feet and the width is 1 foot.