SOLUTION: The perimeter of a rectangle is 2012, and lengths of all sides are integers. What is the smallest possible area of this rectangle?
Algebra.Com
Question 570786: The perimeter of a rectangle is 2012, and lengths of all sides are integers. What is the smallest possible area of this rectangle?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If and are the dimensions of this rectangle, we know that
so and
The area, as a function of x is
That quadratic equation represents a parabola.
Its axis of symmetry is
The maximum area occurs at , when the rectangle is a square.
Moving away from that point, to either side of , the area decreases.
Since the length of the sides are integers, the minimum will be for and , when one side measures 1 and the other 1005. It is the same solutionm no matter what side length we call x.
The minimum area is 1005.
RELATED QUESTIONS
A rectangle has an area of 81 inches, and its side lengths are integers:
a) What is the... (answered by Alan3354)
the lengths of all sides of a triangle are integers greater than 3.
what is the... (answered by jim_thompson5910)
A rectangle has integer side lengths. One pair of opposite sides is increased by 30% and... (answered by jsmallt9)
the lengths of two sides of a rectangle are consecutive odd integers. the perimeter is... (answered by jojo14344)
The lengths of the sides of a rectangle are consecutive even integers. If the perimeter... (answered by josgarithmetic)
The height and the base of a rectangle are positive integers. When the height is
doubled (answered by Fombitz)
The length of all sides of a triangle are integers greater than 3.What is the smallest... (answered by Alan3354)
Please help me solve this word problem:
A rectangle has area of 100 square inches, and (answered by KMST)
A rectangle has a perimeter of 10. If the lengths of its sides are integers, enumerate... (answered by richard1234)