What is the area of a square two of whose sides have lengths x-1 and 5-x?

Answer 1

Squares have all four sides congruent. So if one side is x-1 and the other side is 5 - x, then x-1 and 5-x must be equal since all the sides in a square are equal.

x-1 = 5 - x

Add x to both sides

2x - 1 = 5

Add 1 to both sides

2x = 6

Divide both sides by 2

x=3

If x=3, then one side is 3-1 = 2 units long

The other side should also be 2 units long, but lets check: 5-3 = 2

So both sides = 2 units. So the area is 2 * 2 = 4 square units

Answer 2

Since x-1=5-x, area= (x-1)(5-x)=5x+x^2-5+x=x^2+6x-5 area.