Question
The outer rectangle is shaded. The outer rectangle's length is 2x+2 and the width is 3x-4. The inside rectangle's length is x-3 and the width is x-6. What is the area of the outer rectangle?
Answers
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To find the area of the outer rectangle, we need to multiply its length by its width.
Length of outer rectangle = 2x+2
Width of outer rectangle = 3x-4
Area of outer rectangle = (2x+2) * (3x-4)
Now, we need to subtract the area of the inner rectangle from the area of the outer rectangle to find the shaded area.
Length of inner rectangle = x-3
Width of inner rectangle = x-6
Area of inner rectangle = (x-3) * (x-6)
Shaded area = Area of outer rectangle - Area of inner rectangle
Shaded area = (2x+2) * (3x-4) - (x-3) * (x-6)
Simplifying this expression, we get:
Shaded area = 5x^2 - 16x + 18
Therefore, the area of the outer rectangle is 5x^2 - 16x + 18.
Length of outer rectangle = 2x+2
Width of outer rectangle = 3x-4
Area of outer rectangle = (2x+2) * (3x-4)
Now, we need to subtract the area of the inner rectangle from the area of the outer rectangle to find the shaded area.
Length of inner rectangle = x-3
Width of inner rectangle = x-6
Area of inner rectangle = (x-3) * (x-6)
Shaded area = Area of outer rectangle - Area of inner rectangle
Shaded area = (2x+2) * (3x-4) - (x-3) * (x-6)
Simplifying this expression, we get:
Shaded area = 5x^2 - 16x + 18
Therefore, the area of the outer rectangle is 5x^2 - 16x + 18.
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