Among all rectangles that have a perimeter of 84, find the dimensions of the one whose area is largest. Write your answers as fractions reduced to lowest terms.

Question

Among all rectangles that have a perimeter of 84, find the dimensions of the one whose area is largest.  Write your answers as fractions reduced to lowest terms.

KyledaGreat · Answer

@vocaloid

AZ · Answer

A rectangle has the largest area when it's a square.

Remember, all squares are rectangles but not all rectangles are squares.

As an example, let's take a rectangle with a perimeter of 20.

We could have a length of 6 and a width of 4. The area would be 24
If we had a length of 7 and a width 3, then the area would be 21
If we had a length of 8 and a width of 2, the area would be 16
If we had a length of 9 and a width of 1, the area would be 9

If we had a length of 5 and a width of 5
(this is a square now)
the area would be 25

the area will be the largest when it is a square

AZ · Answer

So your rectangle has a perimeter of 84

What dimensions will give the largest area?

Remember, we said that when it is a square, it will have the largest area. And squares have 4 sides of equal length