As shown in the figure, a trapezoidal Street garden is divided into two parts: parallelogram and triangle. Peony and rose are planted respectively. Peony covers an area of 300 square meters, and rose covers an area of how many square meters?
A: Rose covers an area of 150 square meters
The park has an equilateral triangle with a side length of 2, which is now lawn
There is a point E on the AC side of triangle ABC and a point D on the AB side. De divides the lawn into two parts with equal area. (1) let ad = x (x is greater than or equal to 0), ed = y, and find the functional relation of Y expressed by X
(2) What is the location of the maximum and minimum of de?
(1) In △ ade, y2 = x2 + ae2-2x · AE · cos, 60 ° y2 = x2 + ae2-x · AE, 1
And s △ ade = s △ ABC = A2 = x · AE · sin60 ° x · AE = 2. ②
② Y 2 = x 2 + - 2 (Y > 0), y = (1 ≤ x ≤ 2)
(2) If De is water pipe, y = ≥,
If and only if x 2 =, i.e. x = then "=" holds, so de ‖ BC, and de =
If De is a tour route, f (x) = x2 +
The function decreases on [1,] and increases on [, 2],
So f (x) max = f (1) = f (2) = 5
When De is ab or AC, De is the longest
For a lawn with a length of 16 meters and a width of 9 meters, a stone road with a width of 1 meter should be paved around the lawn. It takes 60 kg of stones per square meter. How many kg of stones do you need to pave this road
(16 + 1 + 1) * (9 + 1 + 1) = 198 (M2)
198-16 * 9 = 54 (M2)
54 * 60 = 3240 (kg)