promotion image of download ymail app
Promoted
hihi
Lv 5
hihi asked in 科學及數學數學 · 10 years ago

數學問題 40分

A rectangle is to be inscribed in the circle x^2+y^2=36. Find the largest possible area of this rectangle.

(請用中文解答,謝謝)

3 Answers

Rating
  • 10 years ago
    Favorite Answer

    A rectangle is to be inscribed in thecircle x^2+y^2=36. Find the largest possible area of this rectangle.Sol設長方形兩對角線夾角w=>長方形面積=4*(1/2)*6*6*Sinw=72Sinw當w=π/2最大面積=72Sin(π/)=72

    • Commenter avatarLogin to reply the answers
  • Nice
    Lv 6
    10 years ago

    圓形的公式: x^2+y^2=36 , 所以半徑(diameter)係6.

    一個圓入面要畫一個最大既長方形,

    長方形的對角線=圓形的直徑=6*2

    假設夾角係theta

    長方形的長及闊分別係12*sin(theta) 及12*cos(theta)

    長方形的面積=長*闊=12*sin(theta)*12*cos(theta)

    =144*sin(theta)*cos(theta) #已知 2sin(theta)cos(theta)=sin(2*theta)

    =72sin(2*theta)

    已知sin(x) 的最大值為 1, sin(2*theta) <=1

    所以, 長方形的面積=72*1=72

    • Commenter avatarLogin to reply the answers
  • 10 years ago

    考慮 x, y >= 0

    長方形面積 = 4xy = 2(2xy) <= 2(x^2+y^2) = 2(36) = 72

    • Commenter avatarLogin to reply the answers
Still have questions? Get your answers by asking now.