For what whole number values of length and width will the rectangle have an area of 60 square yards and I'm perimeter of 38 yards?
To find the whole number values of the length and width that will satisfy the given conditions, we can set up a system of equations.
Let's denote the length as L and the width as W.
From the given information, we know that the area of the rectangle is 60 square yards, so we have the equation:
L * W = 60
We also know that the perimeter of the rectangle is 38 yards, which can be represented by the equation:
2L + 2W = 38
To solve this system of equations, we can use substitution or elimination.
Let's use substitution:
1) From the first equation, solve for L:
L = 60 / W
2) Substitute this value of L in the second equation:
2(60 / W) + 2W = 38
Now, we can simplify this equation and solve for W:
120 / W + 2W = 38
To eliminate the denominators, we can multiply the entire equation by W:
120 + 2W^2 = 38W
Rearrange the equation:
2W^2 - 38W + 120 = 0
Now, we have a quadratic equation. We can factor it or use the quadratic formula to find the values of W that satisfy this equation.
Factoring gives:
(W - 6)(2W - 20) = 0
Setting each factor equal to zero, we have two possibilities:
W - 6 = 0 or 2W - 20 = 0
Solving these equations:
W = 6 or W = 10
Now, substitute these values back into the first equation to find the corresponding values of L:
For W = 6:
L = 60 / 6 = 10
For W = 10:
L = 60 / 10 = 6
Therefore, the whole number values of length and width that satisfy the conditions of having an area of 60 square yards and a perimeter of 38 yards are:
Length = 10 yards
Width = 6 yards