Correct option is D
Given:
Let the length of the longer side of the rectangle be L cm.
The shorter side is 18 cm less than the longer side, so the shorter side is (L - 18) cm.
The area of the rectangle is equal to 6 times the perimeter of the rectangle.
Formula Used:
The area of the rectangle is given by: A = L × (L - 18)
The perimeter of the rectangle is given by: P = 2(L + (L - 18)) = 4L - 36
The area is equal to 6 times the perimeter: A = 6 × P
Substituting the formulas for area and perimeter: L × (L - 18) = 6 × (4L - 36)
Solution:
First, expand both sides of the equation:
L × (L - 18) = 6 × (4L - 36)
L² - 18L = 24L - 216
Bring all terms to one side of the equation:
L² - 42L + 216 = 0
L² - (36+6)L + 216 = 0
L² - 36L -6L + 216 = 0
L( L - 36) - 6( L - 36) = 0
(L-36)(L-6) = 0
L = 36 , L = 6
Since the shorter side would be negative if L = 6, the valid solution is L = 36.
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