My pet square ran away so I bought a pet rectangle of the sa

My pet square ran away, so I bought a pet rectangle of the same area. The length of the rectangle is five centimeters more than twice the side of the square; the height of the rectangle is six centimeters less than the side of the square. How long was the side of the square?

Solution

Let us assume length of the side of the square = x

Length of the rectangle is 5 cm more than twice of the square, that is 2x+5.

Height of the rectangle is 6 cm less than the square side, that is x-6

Area of Square = Area of Rectangle

Area of Square = Side * Side = x*x = x^2

Area of Rectangle = Length * width = (2x+5)(x-6)

Putting both area expressions equal.

(2x+5)(x-6)= x^2

FOIL (2x+5)(x-6)

2x^2 -12x +5x -30 =x^2

2x^2 -7x-30 =x^2

Subtracting x^2 from both sides.

2x^2 -x^2 -7x-30 = x^2-x^2

x^2 -7x-30 =0

Factoring quadratic by applying product sum rule.

Product should be -30 and sum=-7.

So, we would get factors -10 and +3.

(x+3)(x-10)=0

Appying zero product rule and set each factor =0

x+3 =0             x-10=0

x=-3           x=10

x was the length of the side of the square. So we would take only positive value. Because length can\'t be negative.

Therefore, length of the side of the square = 10 cm