the width of a credit card is 3 centimeters shorter than the length (L). The area is 46.75 square centimeters. Find the perimeter.
28
28 centimeters is the perimeter
L(L-3) = 46.75
solve for L and W, then
P = 2(L+W)
its 28
To find the perimeter of the credit card, we first need to determine its dimensions.
Let's assume the length of the credit card is L centimeters.
According to the given information, the width of the credit card is 3 centimeters shorter than the length. Therefore, the width would be (L - 3) centimeters.
We also know that the area of the credit card is 46.75 square centimeters. The formula for calculating the area of a rectangle is A = length × width. So, we can write the equation:
46.75 = L × (L - 3)
Now, let's solve this equation to find the value of the length (L).
46.75 = L^2 - 3L
Rearranging the equation:
L^2 - 3L - 46.75 = 0
Now, we can use the quadratic formula to find the value of L. The quadratic formula is:
L = (-b ± √(b^2 - 4ac)) / 2a
Comparing with our equation:
a = 1, b = -3, c = -46.75
Using the quadratic formula:
L = (-(-3) ± √((-3)^2 - 4 × 1 × (-46.75))) / (2 × 1)
Simplifying:
L = (3 ± √(9 + 187)) / 2
L = (3 ± √196) / 2
L = (3 ± 14) / 2
Now, we have two possible values for L:
1. L = (3 + 14) / 2 = 17 / 2 = 8.5
2. L = (3 - 14) / 2 = -11 / 2 = -5.5
Since a negative value doesn't make sense in this context, we discard the second solution. Therefore, the length of the credit card is L = 8.5 centimeters.
Now, let's calculate the width using the given information:
Width = L - 3
Width = 8.5 - 3 = 5.5 centimeters
Finally, we can find the perimeter by adding up all the sides of the credit card:
Perimeter = 2 × (Length + Width)
Perimeter = 2 × (8.5 + 5.5)
Perimeter = 2 × 14
Perimeter = 28 centimeters
Therefore, the perimeter of the credit card is 28 centimeters.