Harry Thomson bought a large land in the shape of a rectangle with a circumference of 90 meters. He divided it into three rectangular plots. The shorter side has all three plots of equal length, their longer sides are three consecutive natural numbers. Find out the dimensions of each plot and the area of the whole plot.

Correct answer:

a1 =  11 m
b1 =  12 m
c1 =  13 m
y1 =  9 m
S1 =  324 m2
a2 =  12 m
b2 =  13 m
c2 =  14 m
y2 =  6 m
S2 =  234 m2
a3 =  13 m
b3 =  14 m
c3 =  15 m
y3 =  3 m
S3 =  126 m2

Step-by-step explanation:

o=90 m o=2y+2 (a+b+c) o=2y+2 (a+a+1+a+2) o=2y+2 (3a+3) 90=2 y+6 (a+1) a>0,y>0,a>y a1=11;y1=9=11 m a2=12;y2=6 a3=13;y3=3
b1=a1+1=11+1=12 m
c1=a1+2=11+2=13 m
S1=y1 (a1+b1+c1)=9 (11+12+13)=324 m2
b2=a2+1=12+1=13 m
c2=a2+2=12+2=14 m
S2=y2 (a2+b2+c2)=6 (12+13+14)=234 m2
b3=a3+1=13+1=14 m
c3=a3+2=13+2=15 m
S3=y3 (a3+b3+c3)=3 (13+14+15)=126 m2   Verifying Solution:  o1=2 (y1+a1+b1+c1)=2 (9+11+12+13)=90 m o2=2 (y2+a2+b2+c2)=2 (6+12+13+14)=90 m o3=2 (y3+a3+b3+c3)=2 (3+13+14+15)=90 m

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