Length-to-width 3175

We want to enclose a rectangular garden whose length-to-width ratio is 2:1 and whose half of the perimeter borders the road. The fencing path along the road costs 7 euros per meter, and the other fencing costs only 3 euros per meter. How many acres does a garden have if its fencing costs 363 euros?

Correct answer:

a =  24.2 m
b =  12.1 m
S =  2.9282 a

Step-by-step explanation:

a=2b
7·(a+b)+3·(a+b) =363

a=2·b
7·(a+b)+3·(a+b) =363

a-2b = 0
10a+10b = 363

Pivot: Row 1 ↔ Row 2
10a+10b = 363
a-2b = 0

Row 2 - 1/10 · Row 1 → Row 2
10a+10b = 363
-3b = -36.3


b = -36.3/-3 = 12.1
a = 363-10b/10 = 363-10 · 12.1/10 = 24.2

a = 121/5 = 24.2
b = 121/10 = 12.1

Our linear equations calculator calculates it.

$S=a\cdot b/100=24.2\cdot 12.1/100=2.9282\text{a}$

Try another example