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 each plot's dimensions and the whole plot's area.

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 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=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

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators
Do you have a system of equations and looking for calculator system of linear equations?
Do you solve Diofant problems and looking for a calculator of Diofant integer equations?

We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions: