Your question is: The perimeter of a rectangle is 60 meters. What are the possible lengths of any of the rectangle’s sides if its area exceeds 216 square meters?
The answer would be (12,18)
Answer:
the possible sides of a rectangle is 12, 18
Step-by-step explanation:
given:
The perimeter of a rectangle is 60 meters
find:
What are the possible lengths of any of the rectangle’s sides if its area exceeds 216 square meters?
Perimeter (P) = 60 = 2L + 2W ------eq.1
Area (A) = 216 = L x W ---------------eq.2
you can use any of the two equations to to get L or W
say we use the Area = 216 = L x W
L = 216
W
plugin values to eq.1
60 = 2L + 2W
60 = 2( 216 ) + 2W
W
multiply both sides by W
60W = 2(216) + 2W²
60W = 432 + 2W²
rearrange the equation into a quadratic equation:
2W² - 60W + 432 = 0
now, solve for W
- (-60) ± [tex]\sqrt{(-60)^2 - 4 * 2 * 432}[/tex]
W = --------------------------------------------
2 x 2
W = 60 ± 12
4
W = 12
W = 18
therefore,
the possible sides of a rectangle is 12, 18
