The length of a rectangular frame is represented by the expression 3x + 10, and the width of the rectangular frame is represented by the expression 3x + 6. Write an equation to solve for the width of a rectangular frame that has a total area of 192 square inches. a 9x2 + 48x + 60 = 0 b 9x2 + 48x − 132 = 0 c 3x2 + 48x − 132 = 0 d x2 + 16x + 60 = 0
The length of a rectangular frame is represented by the expression 3x + 10, and the width of the rectangular frame is represented by the expression 3x + 6. Write an equation to solve for the width of a rectangular frame that has a total area of 192 square inches.
a
9x2 + 48x + 60 = 0
b
9x2 + 48x − 132 = 0
c
3x2 + 48x − 132 = 0
d
x2 + 16x + 60 = 0
ANSWER:
To find the equation that solves for the width of a rectangular frame with a total area of 192 square inches, we need to set up an equation using the expressions for the length and width of the frame.
The area of a rectangle is given by the formula A = length * width. In this case, the area is given as 192 square inches, and the expressions for the length and width are 3x + 10 and 3x + 6, respectively.
So, we can set up the equation:
(3x + 10) * (3x + 6) = 192
Expanding and simplifying this equation gives us:
9x^2 + 48x + 60 = 192
Rearranging the terms, we have:
9x^2 + 48x - 132 = 0
Therefore, the correct equation to solve for the width of the rectangular frame is:
b) 9x^2 + 48x - 132 = 0
IMPORTANT:
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