Rectangles

The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?

Correct answer:

x =  9 m
a =  11 m
b =  12 m
c =  13 m

Step-by-step explanation:


2·x+2·(a+b+c) = 90
b = a+1
c = b+1
a = 22/2

2a+2b+2c+2x = 90
a-b = -1
b-c = -1
2a = 22

Row 2 - 1/2 · Row 1 → Row 2
2a+2b+2c+2x = 90
-2b-c-x = -46
b-c = -1
2a = 22

Row 4 - Row 1 → Row 4
2a+2b+2c+2x = 90
-2b-c-x = -46
b-c = -1
-2b-2c-2x = -68

Row 3 - 1/-2 · Row 2 → Row 3
2a+2b+2c+2x = 90
-2b-c-x = -46
-1.5c-0.5x = -24
-2b-2c-2x = -68

Row 4 - Row 2 → Row 4
2a+2b+2c+2x = 90
-2b-c-x = -46
-1.5c-0.5x = -24
-c-x = -22

Row 4 - -1/-1.5 · Row 3 → Row 4
2a+2b+2c+2x = 90
-2b-c-x = -46
-1.5c-0.5x = -24
-0.6667x = -6


x = -6/-0.66666667 = 9
c = -24+0.5x/-1.5 = -24+0.5 · 9/-1.5 = 13
b = -46+c+x/-2 = -46+13+9/-2 = 12
a = 90-2b-2c-2x/2 = 90-2 · 12-2 · 13-2 · 9/2 = 11

a = 11
b = 12
c = 13
x = 9

Our linear equations calculator calculates it.



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?

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

Related math problems and questions: