Question

The area of a square is (25x2 + 30x + 9) square units.

Find the perimeter as a binomial.
"Write your answer with no spaces."

Answer 1

Let's assume that the side of the square be x units . We also knows that

• Area of Square = S²
• Perimeter of Square = 4S

Where , S is the side of the square

Now , as per question ;

`{:\implies \quad \sf x^(2)=25x^(2)+30x+9}`

`{:\implies \quad \sf x^(2)=(5x)^(2)+2\cdot 5x\cdot 3 + (3)^(2)}`

`{:\implies \quad \sf x^(2)=(5x+3)^(2)\quad \qquad \{\because (a+b)^(2)=a^(2)+2ab+b^(2)\}}`

Raising power to 1/2 on both sides will give us

`{:\implies \quad \sf x=\pm (5x+3)}`

But , as length can never be -ve . So ;

`{:\implies \quad \bf \therefore \quad x=(5x+3)}`

Now , we have the side of the square , now finding perimeter ;

`{:\implies \quad \sf Perimeter=4(5x+3)}`

`{:\implies \quad \bf \therefore \quad Perimeter=20x+12 \:\: units}`

Hence , The required perimeter is 20x + 12 units :D