Dimensions

Question

The length of a rectangle is
5 ft
less than twice the width, and the area of the rectangle is
33 ft2
. Find the dimensions of the rectangle.

Answer 1

Let us say that the width of this rectangle is some value x.  Since the length of the rectangle is 5 feet less than twice the width, we know that the length must be 2x-5.  Given the length and width in terms of x, we can set up an equation using the formula of area, to find the value of x.  Since we know that the area of the rectangle is 33ft, and we know that the formula for area is A=L x W, we can plug in our current value for length and width in the formula to get : (x)(2x-5) = 33.  By multiplying x to 2x-5, we see that 2x² - 5x = 33.  Notice that we now have a quadratic equation.  Moving the 33 to the left side of the equation, thus setting it to zero, we can find the value of x.  Using the quadratic formula, we see that the two values for x that we got are x=-3 and x= 5.5.  However, since measurement cannot be negative, we can disregard x=-3 and only look at x= 5.5.  We already established that the width is the value of x.  So, the width is 5.5 ft.  To calculate the length, we can simply plug in 5.5 for x in 2x-5.  We see that the length is 6ft.  Thus, finding the dimensions of the rectangle.