Solve the following: 13. You are designing a gift card that has a border along one side, as shown in blue....

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Solve the following:
13. You are designing a gift card that has a border along one side, as shown in blue. The area of the white part of the card is 30 square centimeters. What is the area of the border?

SnapAndSolve AI · Accepted Answer

To find the area of the border, we first need to determine the dimensions of the white part of the card. The white part has an area of 30 square centimeters and dimensions of x cm by (x + 1) cm. Therefore, we have the equation:

x(x + 1) = 30

Solving for x, we get:

x^2 + x - 30 = 0
Using the quadratic formula, x = [-b ± √(b² - 4ac)] / 2a, where a = 1, b = 1, c = -30:
x = [-1 ± √(1 + 120)] / 2
x = [-1 ± √121] / 2
x = [-1 ± 11] / 2
x = 5 or x = -6

Since x must be positive, x = 5 cm.

The total width of the card is (x + 1) + 2 = 8 cm, and the height is x = 5 cm.

The total area of the card is:

Total area = 8 * 5 = 40 square centimeters

The area of the border is:

Area of the border = Total area - Area of the white part = 40 - 30 = 10 square centimeters

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Solve the following: 13. You are designing a gift card that has a border along one side, as shown in blue....

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