The length and width of a rectangle are consecutive odd integers. the area of the rectangle is 63 square units. what are the length and width of the rectangle?

The area of a rectangle is A = L * W.  That's the easy part.  Determining how to express the length and width given the info we were given is the tricky part.  Consecutive means that the numbers are next to each other.  If the consecutive numbers are odd, then they are the odd numbers in order.  Let's pick an example to use to help us set up the expressions for L and W.  Let's use the first consecutive odd integers 1 and 3.  If length is x and x = 1, in order to get from 1 to 3 we have to add 2.  That means that the width is x + 2.  Do that with any consecutive odd numbers and the rule holds true.  Length is x and width is x+2.  We need to multiply them to find the values of x that make the area 63. and .  Set the equation equal to 0 and bring the 63 over by subtraction to factor the polynomial.  .  The 2 numbers that add up to +2 and multiply to -63 are 9 and -7.  But of course we know that the 2 things in math that will never EVER be negative are time and distance/length so -7 is out.  That means that x, the length, is 7 and width, x+2, is 9.  7 and 9 are consecutive odd numbers that multiply to 63.  There you go!