How to fence a 160 square meter rectangular flower garden with a 36 meter fence (18 meters long) on one side? Solve quadratic equation with one variable!

How to fence a 160 square meter rectangular flower garden with a 36 meter fence (18 meters long) on one side? Solve quadratic equation with one variable!

Suppose that the width x Length 36-2x and 36-2x is less than or equal to 18 and X is greater than or equal to 9, X (36-2x) = 160 x square-18x + 80 = 0, X1 = 10, X2 = 8, because 8 is less than or equal to 9, x = 10, so the width is 10 meters and the length is 16 meters

As shown in the figure, there is a fence with a length of 24 meters, and one side of the fence (the maximum available length of the wall a is 10 meters) is used to form a rectangular flower bed with a fence in the middle. Let the width ab of the flower bed be x meters, and the area be s meters. 2. (1) find the functional relationship between S and X; (2) if you want to form a flower bed with an area of 45 meters, how long is ab? (3) Can we make a flower garden larger than 45m2? If yes, request the maximum area and explain the enclosure method; if not, please explain the reason

(1) If AB is x meters, BC is (24-3x) meters, then s = x (24-3x) = - 3x2 + 24x. (2) from the condition - 3x2 + 24x = 45 to x2-8x + 15 = 0, we can get X1 = 5, X2 = 3 ∵ 0 ﹤ 24-3x ≤ 10, 143 ≤ x ﹤ 8 ﹤ x = 3, which is not suitable for the problem, and the width of the garden is 5 meters. (3) s = - 3x2 + 24x = - 3 (x2-8x) = - 3 (x-4) 2 + 48 (143 ≤ x ﹤ 8) ﹤ when x = 143, s has the maximum value of 4 8-3 (143-4) 2 = 4623, so it can be enclosed into a flower bed with a larger area than 45m2. Enclosure method: 24-3 × 143 = 10, the length of the flower bed is 10m, the width is 423m, and the maximum area is 4623m2

As shown in the picture, there is a fence with a length of 24 meters. One side uses a wall (the maximum usable length of the wall is 10 meters) to form a rectangular flower garden with a fence in the middle
Let AB be x meters long
(1) If you want to enclose a flower garden with an area of 45 square meters, how many meters is ab long?
(2) Can a 48 square meter garden be enclosed? If yes, explain the enclosure method; if not, explain the reason

Let the length of the flower bed AB, then the width of the flower bed is (24m-ab) / 3. Because there is a fence in the middle of the flower bed, there are three widths, which are divided by three. The equations are as follows: (1) ab × [(24-ab) / 3] = 45ab × [8-ab / 3] = 458ab-ab & # 178; / 3 = 4524ab-ab & # 178; = 135ab & # 178; - 24ab + 135 = 0 (...)