given the figure below. find yhe area of the shaded part if the rectangle if the are of the big rectangle is 6 times the area of the unshaded rectangle
Answers
Answer:
A of unshaded = 2x × x= 2x^2
total A = 6 × 2x^2 = 12x^2
a of shaded = 10x^2
Given : Area of the big rectangle is 6 times the area of the unshaded rectangle
To Find : The area of the shaded part
Solution:
Inner (smaller) rectangle Dimension 2x by x
Area of rectangle = length * breadth
Area of Smaller rectangle = 2x * x = 2x²
Dimensions of bigger rectangle = (2x +3 + 3 ) by ( x + 3 + 3)
= (2x + 6) by (x + 6)
Area of Bigger rectangle = (2x + 6)(x + 6)
= 2x² + 18x + 36
Area of Shaded part = Area of bigger - Area of Smaller
2x² + 18x + 36 - 2x²
= 18x + 36
Area of the big rectangle is 6 times the area of the unshaded rectangle
2x² + 18x + 36 = 6 (2x²)
=> 10x² - 18x - 36 = 0
=> 5x² - 9x - 18 = 0
=> 5x² - 15x + 6x - 18 = 0
=> 5x(x - 3) + 6(x - 3) = 0
=> (x - 3) ( 5x + 6) = 0
=> x = 3 , x = -6/5
Length can not be negative
Hence x = 3
Area of Shaded part = 18x + 36
= 18(3) + 36
= 90 sq unit
The area of the shaded part is 90 sq units
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