SOLUTION: Treena just graduated Med School. How exciting! Her parents wanted to give her a gift to celebrate. They wanted to frame her diploma from the University of Toronto. The diploma it

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Question 1186910: Treena just graduated Med School. How exciting! Her parents wanted to give her a gift to celebrate. They
wanted to frame her diploma from the University of Toronto. The diploma itself is 10 inches by 12 inches.
They thought that a border of equal width makes sense to do. They wanted the area of the border to be
exactly equal to 25% of the area of the diploma. What length should the width of the border be? What would
be the dimensions of the framed diploma?
Answer by CPhill(2189) (Show Source):
You can put this solution on YOUR website!
Here's how to solve this problem:
**1. Area of the diploma:**
The diploma is 10 inches by 12 inches, so its area is 10 * 12 = 120 square inches.
**2. Area of the border:**
The border's area is 25% of the diploma's area, so it's 0.25 * 120 = 30 square inches.
**3. Dimensions of the framed diploma:**
Let 'x' be the width of the border. The framed diploma will have dimensions (10 + 2x) inches by (12 + 2x) inches.
**4. Area of the framed diploma:**
The area of the framed diploma is (10 + 2x)(12 + 2x).
**5. Set up the equation:**
The area of the framed diploma is equal to the area of the diploma plus the area of the border:
(10 + 2x)(12 + 2x) = 120 + 30
(10 + 2x)(12 + 2x) = 150
**6. Expand and simplify the equation:**
120 + 20x + 24x + 4x² = 150
4x² + 44x + 120 = 150
4x² + 44x - 30 = 0
2x² + 22x - 15 = 0
**7. Solve for x using the quadratic formula:**
x = (-b ± √(b² - 4ac)) / 2a
x = (-22 ± √(22² - 4 * 2 * -15)) / (2 * 2)
x = (-22 ± √(484 + 120)) / 4
x = (-22 ± √604) / 4
x = (-22 ± 2√151) / 4
x = (-11 ± √151) / 2
Since x represents a width, it must be positive. Therefore:
x = (-11 + √151) / 2
x ≈ (-11 + 12.288) / 2
x ≈ 1.288 / 2
x ≈ 0.644 inches
**8. Dimensions of the framed diploma:**
* Width: 10 + 2x ≈ 10 + 2 * 0.644 ≈ 11.288 inches
* Height: 12 + 2x ≈ 12 + 2 * 0.644 ≈ 13.288 inches
**Answer:**
The width of the border should be approximately 0.644 inches. The dimensions of the framed diploma would be approximately 11.29 inches by 13.29 inches.