Question

the arean of a square is (x^2-6x+9)sq. unit . find its perimeter with proper process


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Answer 1

Answer:

Perimeter of the square is (x - 3) units.

Step-by-step explanation:

Question says that,

The area of a square is (x² - 6x + 9)units².

We need to find the perimeter of the square.

Step 1 : Find the each side of the square.

We know that,

→ Area of the square = (each side)²

But, the area given is (x² - 6x + 9)units²

So, we can say that

→ (x² - 6x + 9) = (each side)²

→ (x - 3)² = (each side)²

[using identity : a² - 2ab + b² = (a + b)² ]

→ √(x - 3)² = each side

[On transposing √ on L. H. S. ]

→ x - 3 = each side

Each side of the square is (x - 3) units.

Step 2 : Calculate the perimeter

Perimeter of a square is given by :

→ 4 × each side

→ 4 × (x - 3)

→ 4x - 12 units.

The perimeter of the square is (4x - 12)units.