The area of a square is (25x2 + 30x + 9) square units. Find the perimeter as a binomial. "Write your answer with no spaces."

Question

asked Sep 23, 2023 117k views

1 Answer

David Gidony · Answer 1 · 2023-09-29T04:27:56+0000

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

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