If the length of a rectangle is 9m longer than its width the area of the rectangle is 36m sq units find the dimensions of the rectangle?

To solve this problem, you first need to define some variables and then set up an equation. Let w = width of the rectangle and l = length of the rectangle. Since the length is 9 m longer than the width, we can write the following: w = width w + 9 = length Since the area of a rectangle is found by multiplying length x width, we can write the following equation: w(w + 9) = 36 Next, we must solve this equation. By the distributive property, we have w^2 + 9w = 36. Subtracting 36 from both sides, we get w^2 + 9w - 36 = 0 We can factor this trinomial into (w + 12)(w - 3) = 0 By the zero product property, we have w + 12 = 0 or w - 3 = 0 Solving these two equations, we have that w = -12 or w = 3. Since the width of a rectangle cannot be negative, we ignore the w = -12 solution and we find that w = 3. Since our width is 3 m, our length must be 12 m. We can check our answer by verifying that 12 m x 3m = 36 m^2.