perimeter = 26in. what is the length, width and area?

Question

Write length and width that will give the largest area for each perimeter. Alll sides are whole numbers.

Answer 1

Let the length of the rectangle be l, width be w and area be a.

Perimeter of the rectangle is 26in.

Formula for Perimeter of the ractangle is 2(l+b).

By equating we get,

                   [Divide each side by 2]

There are 6 chances of getting 13 by addition. That is 12+1, 11+2, 10+3, 9+4, 8+5, 7+6.

That means length and width may be 12,1; 11,2; 10,3; 9,4; 8,5 and 7,6.

Formula for area of the rectangle is l * b.

Areas for those cases are 12, 22, 30, 36, 40 and 42.

The condition is that the length and width should give the largest area, which can be be possible in only 7,6 case.

Therefore the lengh and width of the rectangle is 7in and 6in respectively

Area of the rectangle is l * b=7 * 6 = 42 square inches.

Therefore the length, width and area of the rectangle are 7 in, 6 in and 42 square inches respectively.