for what whole number values of length and width will the rectangle have an area of 60 square yards and a perimeter of 38 yards?
15 * 4
lw = 60 ---> l = 60/w
2l + 2w = 38 ---> l + w = 19
60/w + w = 19
times w
60 + w^2 = 19w
w^2 - 19w + 60 = 0
(w-15)(w-4) = 0
w = 15 or w = 4 , then
l = 4 or l = 15
the length is 15 and the width is 4
To find the whole number values of length and width that will satisfy the given conditions, we need to use the formula for the area and perimeter of a rectangle.
The area of a rectangle is given by the formula: Area = length x width
The perimeter of a rectangle is given by the formula: Perimeter = 2(length + width)
Given:
Area = 60 square yards
Perimeter = 38 yards
Using these values and the formulas, we can create a system of equations to solve for the length and width.
Equation 1: Area = length x width
60 = length x width
Equation 2: Perimeter = 2(length + width)
38 = 2(length + width)
Now, let's solve this system of equations to find the values of length and width.
From Equation 1, we have:
60 = length x width
We need to find whole number values for length and width, so let's try different combinations.
One possible combination is:
length = 12
width = 5
Plugging these values into Equation 2:
38 = 2(12 + 5)
38 = 2(17)
38 = 34
Since 38 does not equal 34, this combination of length and width does not satisfy the given conditions.
Let's try another combination.
Another possible combination is:
length = 10
width = 6
Plugging these values into Equation 2:
38 = 2(10 + 6)
38 = 2(16)
38 = 32
Again, 38 does not equal 32, so this combination also does not satisfy the given conditions.
We can continue trying different combinations until we find a pair of length and width values that satisfy both equations.
After trying different combinations, we find that there are no whole number values of length and width that result in an area of 60 square yards and a perimeter of 38 yards.
Therefore, there are no whole number values of length and width that satisfy the given conditions.