Respuesta :
To find the width of the frame, we first need to calculate the total area of the photo with the frame included. Given that the surface area of the photo is 77 cm² and the outer dimensions of the photo are 15 cm in length by 11 cm in width, we can set up the following equation:
Total area (photo + frame) = Photo area
(15 + 2x) * (11 + 2x) = 77
Where x represents the width of the frame. Expanding the equation, we get:
165 + 37x + 30x + 4x² = 77
4x² + 67x + 165 = 77
4x² + 67x + 88 = 0
To solve the quadratic equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Where a = 4, b = 67, and c = 88. Substituting these values into the formula, we get two possible solutions for x. Then, we verify which one is the correct solution for the width of the frame.
Total area (photo + frame) = Photo area
(15 + 2x) * (11 + 2x) = 77
Where x represents the width of the frame. Expanding the equation, we get:
165 + 37x + 30x + 4x² = 77
4x² + 67x + 165 = 77
4x² + 67x + 88 = 0
To solve the quadratic equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Where a = 4, b = 67, and c = 88. Substituting these values into the formula, we get two possible solutions for x. Then, we verify which one is the correct solution for the width of the frame.
