Let the side lengths of the tables be x m and y m respectively.

Sum of areas = 14.5m²

x² + y² = 14.5
(Recall area of square is length × length)

Multiply by 4,

4x² + 4y² = 58
4x² = 58 - 4y² ①


Sum of perimeters = 20 m²

4x + 4y = 20
(Recall perimeter of square = 4 lengths)

Divide by 4,

x + y = 5
x = 5 - y

Square both sides,

x² = (5 - y)²
x² = 25 - 10y + y²

Sub this into ①,

4(25 - 10y + y²) = 58 - 4y²

100 - 40y + 4y² = 58 - 4y²

8y² - 40y + 42 = 0

Divide by 2,

4y² - 20y + 21 = 0

(2y - 3)(2y - 7) = 0

2y = 3 or 2y = 7

y = 1.5 or y = 3.5

Then,

x = 5 - 1.5 or x = 5 - 3.5

x = 3.5 or x = 1.5


In a sense, x and y are not unique since we can order it either way.

We can call this an ordered pair (1.5,3.5)

So the lengths are 3.5m and 1.5m