# 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?

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

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