A rectangle's width is 6 FEET less than its length. If the area of the rectangle is 247 square feet. To FIND :The length in feet. Solution :Analysis :Here the formula of area of rectangle is USED. We can see that the length and breadth both are dependent on each other. So we have to form equation through which we can find the length. Required Formula :Area of rectangle = Length × breadthExplanation :Let us assume that the length is "x" ft. Breadth = "x - 6" ft. Area = 247 ft²We know that if we are given the area of the rectangle and is asked to find the length and breadth of the rectangle, Area of rectangle = Length × breadthwhere, Area = 247 ft²Length = x ftBreadth = x - 6 ftUsing the required formula and SUBSTITUTING the required values, ⇒ Area of rectangle = Length × breadth⇒ 247 = x × (x - 6) Expanding the brackets, ⇒ 247 = x² - 6x⇒ 0 = x² - 6x - 247⇒ x² - 6x - 247 = 0Splitting the middle term, ⇒ x² + 13x - 19x - 247 = 0⇒ x(x + 13) - 19(x + 13) = 0⇒ (x - 19)(x + 13) = 0⇒ (x - 19) = 0⇒ x - 19 = 0⇒ x = 19∴ x = 19.⇒ (x + 13) = 0⇒ x + 13 = 0⇒ x = -13∴ x = -13.Dimensions cannot have negative value so we will NEGLECT -13 as one the dimensions. Considering 19 as one of the dimensions, The dimensions :Length = x = 19 ftBreadth = x - 6 = 19 - 6 = 13 ftThe length of the rectangle is 19 feet.Verification :⇒ Area of rectangle = Length × breadth⇒ 247 = 19 × 13⇒ 247 = 247∴ LHS = RHS.Hence verified.