一个长方形长为a,宽为b.若将长增加5分之1宽增加4分之1,则面积增加多少?周长呢?

S增=a*(1+1/5)*b*(1+1/4)-a*b=1/2*ab
L增=1/5*a*2+1/4*b*2=2a/5+b/2

长为a,则增加后的长是a+a/5
宽为b,则增加后的宽是b+b/4
增加后的长方形面积是(a+a/5)b+b/4
未增加的长方形面积是ab
(a+a/5)b+b/4-ab
=(ab+ab/4+ab/5+ab/20)-ab
=(20ab/20+5ab/20+4ab/20+ab/20) (通分母)
=30ab/20-ab
=30ab/20-20ab/20
=3ab/2-2ab/2
=1/2
所以增加后的长方形面积比未增加的长方形面积多1/2
未增加的长方形周长是2a+2b
增加后的长方形周长是2(a+a/5+b+b/4)
(2(a+a/5+b+b/4))-2a+2b
=(2a+2a/5+2b+2b/4)-2a+2b
=(10a/5+2a/5+8b/4+2b/4)-2a+2b
=(12a/5+5b/2)-2a+2b
=(24a/10+25b/10)-2a+2b
=(24a+25b/10)-2a+2b
=24a+25b/10-20a+20b/10
=4a+5b/10
所以增加后的长方形周长比未增加的长方形周长多4a+5b/10

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