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# help

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A rectangle has a perimeter of 30 units and its dimensions are whole numbers. What is the maximum possible area of the rectangle in square units?

Nov 13, 2019

#1
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The formula for area is a*b=c where c is the area and a,b are the length and height

we know that 2a+2b= the perimeter of the shape and simplifying it would be

a+b=15

the best way to get your answer is to look at a graph this graph shows the max it could be and the answer is easy to find because it is literally the middle of the line which is

(7.5,7.5) and that gives you an answer of 56.25

Nov 13, 2019
edited by ChessPlayer  Nov 13, 2019
#4
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Yes, but the sides must be whole numbers

CoolStuffYT  Nov 13, 2019
#2
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If it were a SQUARE with equal sides, it's area would be maximized, but the sides would be 7.5

so I think 8 x 7 would maximize the area of a rectangle  = 56 sq units

Nov 13, 2019
#3
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To make the area as big as possible, we should make each side as close to each other as possible. For example, for perimeter 20, a 5x5 rectangle has more area than a 3x7 because 5 and 5 are close together.

With this, we can easily find that 7+8+7+8, or a 7x8 rectangle, is the most compact rectangle with whole number dimensions.

The area of this is 56 square units.

You are very welcome!

:P

Nov 13, 2019