How many rectangles can be drawn with 38 cm as perimeter? Also ,find the dimensions of the rectangle whose area will be maximum.

A rectangle has two pairs of equal sides. Let's denote the length of one pair of equal sides as "l" and the length of the other pair of equal sides as "w". The perimeter of a rectangle is given by the formula: perimeter = 2l + 2w.

Given that the perimeter is 38 cm, we can write the equation as: 2l + 2w = 38.

To find the maximum area, we need to find the dimensions of the rectangle that will maximize the product of the length and width. The formula for the area of a rectangle is: area = length × width.

Let's solve the equation 2l + 2w = 38 to find the possible dimensions of the rectangle.

Rearranging the equation, we have: l + w = 19.

Now, let's list some possible values for l and w that satisfy the equation.

- l = 1, w = 18

- l = 2, w = 17

- l = 3, w = 16

- l = 4, w = 15

- l = 5, w = 14

- l = 6, w = 13

- l = 7, w = 12

- l = 8, w = 11

- l = 9, w = 10

These are the possible pairs of dimensions that satisfy the equation. For each pair, we can calculate the area by multiplying the length and width.

For example, for l = 1 and w = 18, the area would be 1 × 18 = 18 square cm.

Repeat this calculation for each pair of dimensions and find the pair with the maximum area.

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