Given the figure below. Find the area of the shaded part of the rectangle if the area is 9 square ft, the length and width of the rectangle.
Correct =brainlest
Nonesense =Reported
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Given the figure below. Find the area of the shaded part of the rectangle if the area is 9 square ft, the length and width of the rectangle.
Correct =brainlest
Nonesense =Reported
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Answer:
90 sq. units
Step-by-step explanation:
Solving for the length of the larger and smaller rectangles:
Larger rectangle:
Smaller rectangle:
Area of the larger rectangle
= L₁W₁
= (2x + 6)(x + 6)
= 2x² + 12x + 6x + 36
= 2x² + 18x + 36
Area of the unshaded or smaller rectangle
= L₂W₂
= 2x(x)
= 2x²
Given that the area of the big rectangle is 6 times the area of the unshaded rectangle or the smaller rectangle, we get
2x² + 18x + 36 = 6(2x²)
2x² + 18x + 36 = 12x²
10x² - 18x - 36 = 0
5x² - 9x - 18 = 0
(x - 3)(5x + 6) = 0
x - 3 = 0
x₁ = 3
5x + 6 = 0
5x = -6
x₂ = -6/5
We want x to be positive, so x = 3.
Area of the shaded part
= (Area of the larger rectangle) - (Area of the smaller rectangle)
= L₁W₁ - L₂W₂
= (2x + 6)(x + 6) - 2x(x)
= 2x² + 18x + 36 - 2x²
= 18x + 36
Substituting x = 3, we get
= 18(3) + 36
= 54 + 36
= 90 sq. units