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?

Answer 1

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.