A rectangular garden has a width of 20 feet and a length of 24 feet. If each side of the garden is increased through the similar amount, how many feet is the new length if the new area is 141 square feet more than the original?
Let x = the amount in which each side of the garden is increased. Then, x + 20 = the new width and x + 24 = the new length. Because the area of a rectangle is length times width, after that the area of the old garden is 20 × 24 = 480 and the new area is 480 + 141 = 621. The equation using the new area becomes (x + 20)(x + 24) = 621. Multiply by using the distributive property on the left side of the equation: x2 + 24x + 20x + 480 = 621; combine like terms: x2 + 44x + 480 = 621. Subtract 621 from both sides: x2 + 44x + 480 - 621 = 621 - 621; simplify: x2 + 44x - 141 = 0. Factor the trinomial: (x - 3)(x + 47) = 0. Set each factor equal to zero and solve: x - 3 = 0 or x + 47 = 0; x = 3 or x = - 47. Reject the negative solution because you won't have a negative increase. Therefore, each side will be increased through 3 and the new length would be 24 + 3 = 27 feet.