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Basic inequality if the perimeter of a right triangle is t, then the maximum area of the right triangle is t
Let the area of an isosceles right triangle be the largest! Let the length of the right side be x, then the length of the hypotenuse is t-2x. From the Pythagorean theorem, we can get: 2x & sup2; = (t-2x) & sup2;, X1 = [2T + √ (2t & sup2;)] / 2 [rounding off], X2 = [2T - √ (2t & sup2;)] / 2. The largest area is: X & sup2; = {[2T - √ (2t & sup2;)] /
Why can mean inequality be used to find the maximum area of a right triangle when its perimeter is 10
If one side of the right angle is x and the other side is y, x + y is not a fixed value, x + y + √ (x ^ 2 + y ^ 2) = 10 ≥ 2 √ (XY) + √ (2XY)
Why can mean inequality be used
If x > 0, Y > 0, then x + Y > = 2 √ (XY) can be used
And (x ^ 2 + y ^ 2) > = 2XY can be used at any time, no matter x > 0 or Y > 0
If the radius of a is 10m, when the radius decreases x (m), the area of the circle decreases y (M & sup2;). Y is a function of X. write out the analytic formula of the function to fit it
y=π(10-x)^2 （x
If the radius of a circle is 4cm, and the radius increases by xcm, the area of the circle increases by y2cm. Find the functional relationship between Y and X
y = π(x+4)^2-π*4^2 = πx^2+8πx+16π-16π = πx^2+8πx
RELATED INFORMATIONS
- 1. Change the area s of a circle into a function of the circumference C of a circle
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- 3. As shown in the figure, the vertex of square mnpq is on the edge of triangle ABC. When SC = A and high ad = h satisfy what conditions, square Mn
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- 6. The circumference of a rectangle is 20 cm. If the length is 9 cm, the width is 1 cm. If the length is 8 cm, the width is 2 cm With the same perimeter Judge whether it is an inverse proportion and state the reasons
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- 8. The area of a triangle is 96 square centimeters. If the bottom and height of the triangle increase by one third, this is the area of the triangle The area of a triangle is 96 square centimeters. If the bottom and height of the triangle increase by one third, what is the area of the triangle?
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- 12. The perimeter of an equilateral triangle is 15 cm, the height is 3.5 cm, and its area is ()
- 13. What is the area of an equilateral triangle with a circumference of 12 cm?
- 14. The perimeter of an equilateral triangle is 18 cm, the height is 3.6 cm, and its area is______ Square centimeter
- 15. The perimeter of an equilateral triangle is 15 cm and its height is 4 cm. What's its area () square cm
- 16. An equilateral triangle has a circumference of 15 cm and a height of 4.4 cm. What is the area of the triangle?
- 17. If the perimeter of a rectangle is 38cm and the length is 1cm more than the width, the length of the rectangle is______ cm．
- 18. In RT △ ABC, the sum of two right angle sides AB and AC is 8. Let BC = x, find the function of area s of RT △ ABC with respect to X and the value range of X
- 19. If the waist length of an isosceles triangle is 13 and the bottom length is 10, its area is () A. 65B. 60C. 120D. 130
- 20. Is the correspondence between the perimeter set L and the area set a of a square a function and why? Is the correspondence between the perimeter set and the area set of a triangle a function and why?