Question

A rectangular park 30m by 20m is increased on all sides by the same amount. Its area increases by 1400m^(2). By how much is each dimension increased?

Answer 1

....x = the length of increase Initial area = 30*20=600m²

we increase the length by x m= 30+x

we increase the width by xm = 20+x

new area: (30+x)(20+x)=

600+30x+20x+x²=

x²+50x+600

and the new area is increased by 1400m²

x²+50x+600=1400+600

x²+50x+600-1400-600=0

x²+50x-1400=0

b²-4ac =50²-4(1*-1400)= 8100

delta=8100; V-delta = 90

(-b-Vdelta)= (-50-90)/2=-70

(-50+90)/2=20

a length is never negative, x=20

new length: 50

new width = 40

new area = 50*40=2000m²

% increase:

new length: 50 : [(50-30)/30]*100=66,6666= 66,7%

new width = 40 : [(40-20)/20]*100=100%

Explanation: