the area of rectangle abcd is 9cm²
show that x²+5x=3

Step-by-step explanation:

The rectangle has been divided into a square and three rectangles.

The area of

a square = (x)(x) = x²

a rectangle #1 = (2)(x) = 2x

a rectangle #2 = (3)(x) = 3x

a rectangle #3 = (2)(3) = 6

The area of a large rectangle is the sum of the square area and three rectangles, and is 9 cm². Therefore we have the equation:

x² + 2x + 3x + 6 = 9     subtract 6 from both sides

x² + 5x + 6 - 6 = 9 - 6

x² + 5x = 3