中四a maths 一問

As follows:

圖片參考：http://farm3.static.flickr.com/2289/2078004730_837742e9c9_m.jpg

The area of rectangle ABCD:
6 x 8 = 48 cm^2
The area of triangle APS and QRC:
2x ( 6 - x ) / 2 = x ( 6 - x ) cm^2
The area of triangle SRD and PQB:
2x ( 8 - x ) / 2 = x ( 8 - x )
Then,
A = 48 - x ( 6 - x ) - x ( 8 - x )
= 2x^2 - 14x + 48
= 2 ( x^2 - 7x ) + 48
= 2 ( x^2 - 7x + 49 / 4 ) + 48 - 2 ( 49 / 4 )
= 2 ( x - 7 / 2 )^2 + 47 / 2
So the value os x is 7 / 2 when A is a min.

2007-12-01 20:32:51 補充：
Sorry for a typing error, the last line is So the value of x is 7 / 2 when A is a min.

ans:7/2