Complete question :
Kayla is framing a square painting with side lengths of x+5 inches. The total area of the painting and the frame has a side length of 3x-6. inches. Write an expression for the area of the frame. Then find the cost of the material for the frame if x = 16. The material for the frame will cost 0.07 per square inch
Answer:
8x² - 46x + 11 ;
$92.61
Explanation:
Side length of square painting = x + 5
Area of square painting = (x +5)²
Side length of Total area of square painting + frame = 3x - 6
Total area = (3x - 6)²
Area of frame :
(3x - 6)² - (x +5)²
(3x - 6)(3x-6)
9x² - 18x - 18x +. 36 = 9x² - 36x + 36
(x +5)(x+5) = x²+5x+5x+25 = x² + 10x + 25
9x² - 36x + 36 - (x² + 10x + 25)
9x² - 36x + 36 - x² - 10x - 25
8x² - 46x + 11
Area of frame = 8x² - 46x + 11
8(16^2) - 46(16) + 11
= 1323 in²
1323 * 0.07 = $92.61