the perimeter of a rectangle is 40 feet and its area is 96 square feet. find the length and width?
2L + 2W = 40
Divide both sides of first equation by 2.
L + W = 20, Then W = 20 - L
L * W = 96
Substitute 20-L for W in second equation and solve for L. Insert that value into the first equation and solve for W. Check by inserting both values into the second equation.
To find the length and width of the rectangle given its perimeter and area, we can set up a system of equations.
Let's assume the length of the rectangle is "L" and the width is "W".
We know that the perimeter of a rectangle is given by the formula:
Perimeter = 2(L + W)
And we are given that the perimeter is 40 feet, so we have:
40 = 2(L + W) ----(Equation 1)
We also know that the area of a rectangle is given by the formula:
Area = Length x Width
And we are given that the area is 96 square feet, so we have:
96 = L x W ----(Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) that we can solve simultaneously to find the values of L and W.
From Equation 1, we can simplify it to:
20 = L + W ----(Equation 3)
Now we can solve this system of equations, either by substitution or elimination method.
Let's use substitution method.
We rearrange Equation 3 to solve for L:
L = 20 - W
Substitute this value of L into Equation 2:
96 = (20 - W) x W
Expand and rearrange:
96 = 20W - W^2
Rearrange it to a quadratic equation:
W^2 - 20W + 96 = 0
Now we can solve this quadratic equation. We can do it by factoring, completing the square, or using the quadratic formula.
If we factor it, we get:
(W - 8)(W - 12) = 0
So, W can either be 8 or 12.
If we substitute these values of W back into Equation 3, we can find the corresponding values of L:
For W = 8, using Equation 3:
20 = L + 8
L = 20 - 8
L = 12
So, one possible solution is L = 12 and W = 8.
For W = 12, using Equation 3:
20 = L + 12
L = 20 - 12
L = 8
So, the other possible solution is L = 8 and W = 12.
Therefore, the length and width of the rectangle can be either L = 12 ft and W = 8 ft, or L = 8 ft and W = 12 ft.