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The maximum area of ​​a rectangle with the sum of the base and height (¡¿ 2) being constant

ÀÛ¼ºÀÚ Uploader : ¾îÁ¦Ã³·³ ÀÛ¼ºÀÏ Upload Date: 2019-01-23º¯°æÀÏ Update Date: 2019-01-24Á¶È¸¼ö View : 357

As shown in the figure, when the sum of the base length b and the height h is constant, the maximum area of ​​the rectangle can be obtained as follows.

L = b+2*h ¡æ h = (L-b)/2

A = b*h = b*(L-b)/2 = -(1/2)b^2 + (1/2)*L*b

As the area A is the quadratic equation for b, and the coefficient of b^2 is a negative value, the equation of area A has a maximum value.

When the area A becomes the maximum,

b = (1/2)*L

h = (1/4)*L

Thus, the maximum area is:

Amax = (1/8)*L^2

*** Âü°í¹®Çå[References] ***

Amax = (1/8)*L^2
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