Section width 2.2 m. Find the width of another section with the same perimeter if its length is 0.3 m

Section width 2.2 m. Find the width of another section with the same perimeter if its length is 0.3 m less than the length of the first section.

Let a₁, – the length of the first section, b₁ – its width.
Let a₂, b₂ be the length and width of the second section.

Then:
2 ∙ (a₁ + b₁) = P₁ – the perimeter of the first section.
2 ∙ (a₂ + b₂) = P₂ – the perimeter of the second section.

By the condition of the problem, the perimeters are equal, the width of the first is given, and the length of the second is 0.3 meters less than the length of the first section:
P₁ = P₂;
b₁ = 2.2;
a₁ – a₂ = 0.3;

We got a system of equations:
1) 2 ∙ (a₁ + b₁) = P₁;
2) 2 ∙ (a₂ + b₂) = P₂;
3) a₁ – a₂ = 0.3;
4) b₁ = 2.2;
5) P₁ = P₂;

Let us subtract equation (2) from equation (1):
2 ∙ (a₁ + b₁) – 2 ∙ (a₂ + b₂) = P₁ – P₂;
2 ∙ [(a₁ – a₂) + (b₁ – b₂)] = P₁ – P₂;

Substitute the values ​​from equations (3), (4), (5):
2 ∙ [0.3 + 2.2 – b₂)] = 0 ⇔
⇔ 2 ∙ (2.5 – b₂) = 0 ⇔
⇔ 5 – 2 ∙ b₂ = 0 ⇔
⇔ 5 = 2 ∙ b₂ ⇔
⇔ b₂ = 2.5;

Answer: the width of the second section is 2.5 meters.