Verified answer

The dimension of the rectangular table is 7 m by 4 m.

Step-by-step explanation:

Step 1: Formulate an equation using the formula for the perimeter of the rectangle.

The perimeter of a rectangle is given by the formula:

P = 2l + 2w

where: P - perimeter

l - length

w - width

Substitute the value of P which is 64 in the equation

22 = 2l + 2w

Simplify

11 = l + w

Equate to w

w = 11 - l

Step 2: Formulate an equation using the formula for the area of the rectangle.

The area of a rectangle is given by the equation:

A = l x w

where: A - area

l - length

w - width

Substitute the value of A which is 28 in the equation

28 = l x w

Equate to w

w = 28/l

Step 3: Compare the two equations and solve for length.

w = w

11 - l = 28/l

Simplify

11l - l² = 28

Equate to zero

l² - 11l + 28 = 0

Factor the equation

(l - 4)(l - 7) = 0

l1 = 4 | l2 = 7

Considering that length is the longest side of the rectangle, length = 7

Step 4: Solve for w using any of the two equations

w = 11 - l

w = 11 - 7

w = 4

The dimension of the rectangular table is 7 m by 4 m.

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