![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
In the "old city reconstruction", a city plans to plant some kind of turf on a triangular open space as shown in the figure to beautify the environment. It is known that ab = 30m, AC = 40m, ∠ BAC = 150 ° and the price of this kind of turf is a yuan per square meter. How much is it required to buy this kind of turf at least?
As shown in the figure, make the height CD of Ba side, let the extension line intersect with BA at the point D, ∵ BAC = 150 °, ∵ DAC = 30 °, ∵ CD ⊥ BD, AC = 40m, ∵ CD = 20m, ∵ AB = 30m, ∵ s △ ABC = 12ab × CD = 12 × 30 × 20 = 300m2, ∵ the selling price per square meter is a yuan, and the purchase price is at least 300A yuan
If the price of turf is a yuan per square meter in the open space, if AB = 20m, AC = 30m and ∠ a = 150 ° are known, it is necessary to buy turf
A. 450A yuan b.225a yuan c.150a yuan d.300a yuan
Lengthen Ca and make BD perpendicular to Ca intersection point D
Because,
In the old city reconstruction of a city, it is planned to plant turf on a triangular open space as shown in the figure to green the environment. It is known that the price of such turf is a yuan per square meter, so it is at least necessary to buy such turf______ &RMB
Let BD = XM, then CD = (15-x) M. in RT △ abd, ad2 = ab2-bd2, in RT △ ACD, ad2 = ac2-cd2, so ab2-bd2 = ac2-cd2, that is 132-x2 = 142 - (15-x) 2, the solution is x = 6.6, then ad2 = 132-x2 = 125.44, ad = 11.2, s △ ABC = 12bc · ad = 12 × 15 × 11.2 = 84. Since the price of turf per square meter is a yuan, it needs at least 84A yuan to buy this kind of turf The answer is 84A
RELATED INFORMATIONS
- 1. Can 15 meters, 16 meters and 17 meters form a triangle? What's the area?
- 2. The area of the trapezoid is 2 hectares. How many meters is the bottom of the trapezoid
- 3. If the side length of a square garden covering 4 hectares is reduced by 10 meters, how many square meters will the area of the garden be reduced
- 4. A trapezoidal vegetable field, with an area of 270 square meters, has a top bottom of 28 meters and a bottom of 32 meters. How high is it
- 5. The area of a trapezoidal orchard is about 2.4 hectares. Its top bottom is 320 meters long and its bottom is 180 meters long. How high is the trapezoidal orchard?
- 6. There is a square orchard covering an area of 1 hectare. If its sides are extended by 200 meters, how many hectares will the area of the orchard increase?
- 7. There is a rectangular wheat field, 900 meters long and 400 meters wide, with a total yield of 194400 kg of wheat. How many kg of wheat are harvested per hectare on average?
- 8. A triangle nursery with an area of 2.1 hectares is 700 meters long at the bottom. How many meters high is it? A triangle nursery with an area of 2.1 hectares is 700 meters long at the bottom and how high is it
- 9. A parallelogram of cotton field, the bottom is 120 meters, the height is 150 meters. (calculator can be used) this cotton field area? How many hectares? If A parallelogram of cotton field, the bottom is 120 meters, the height is 150 meters What is the area of this cotton field? How many hectares? If the average yield of cotton per hectare is 1500 kg, how many kg of cotton can be produced?
- 10. A street garden covers three fourths of an hectare, half of which are lawns, 20% are flower beds, and the rest are sidewalks What are the total area of lawn and flower bed? & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; what are the total area of lawn and flower bed; 3.
- 11. In the "old city reconstruction" of a city, it is planned to plant turf on a triangular open space in the city as shown in the figure to beautify the environment Planting turf to beautify the environment is known to cost 80 yuan per square meter. How much does it cost to buy this kind of turf?
- 12. As shown in the figure, the shaded part represents the campus lawn, the blank part represents the path, and the algebraic expression is used to represent the lawn area
- 13. There are three lawns in the street garden. The first one accounts for 3 / 10 of the total area, the second one covers 1 / 5 of the total area, and the third one accounts for 1 / 3 of the total area. What is the total area of the three lawns in the street garden?
- 14. There is a triangle lawn in the middle of the road (see photo). The price of 1 m2 lawn is 12 yuan. How much does it cost to grow this lawn?
- 15. Pythagorean theorem] if the length of the hypotenuse of an isosceles right triangle is 4, then the perimeter of the right triangle is 4 It's a process
- 16. The perimeter of a rectangular lawn is 36m. If its length and width increase by 3M, how many square meters will the original lawn area increase?
- 17. The perimeter of a rectangular lawn is 36m. If its length and width increase by 3M, how many square meters will the original lawn area increase?
- 18. As shown in the figure, to build a lawn with equal radius at each of the three corners of the triangle square ABC, the radius of the fan should be 20 meters, and the total area of the lawn should be calculated. (π = 3.14)
- 19. A school takes an equilateral △ ABC corner with a side length of 2A The corner of an equilateral △ ABC with a side length of 2a is divided into two parts with equal area by de. D is on AB and E is on AC (1) Let ad = x (x ≥ a), ed = y, find the functional relation of Y expressed by X;? (2) If De is the location of irrigation water pipe, in order to save money, I hope it is the shortest, where should de be? If De is the tour line, I hope it is the longest, where should de be? The answer is (1) y = √ (x ^ + 4 * (a ^ 4) / x ^ - 2A ^) (2) When ad = (√ 2) * A and de ‖ BC, De is the shortest; when D is the midpoint of AB, e coincides with C or D coincides with B, e is the midpoint of AC, De is the longest Mainly the first question
- 20. A rectangular grassland is 16 meters long and 8 meters wide, with a stone road in the middle. If it costs 40 yuan to pave a 1 square meter grassland, how much does it cost to pave this land The back is the floor. How much is it?