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