Question

The area of a square is 4x² + 20x+25,which expression represent a side of the square.​

Answer 1

Answer:

area of square=side²

4x²+25x+25=(2x)²+2x5x2x+5²=(2x+5)²

therefore side of square=2x+5

Answer 2

GIVEN :-

The area of a square is 4x² + 20x + 25 units.

TO FIND :-

The expression which represents side of the square .

SOLUTION :-

Firstly we will simplify the expression of area of a square by using "splitting the middle term" Process.

⇒ Area of square = 4x² + 20x + 25

⇒ Area of square = 4x² + 10x + 10x + 25

⇒ Area of square = 2x(2x + 5) + 5(2x + 5)

⇒ Area of square = (2x + 5)(2x + 5)

⇒ Area of square = (2x + 5)² units ².

Now as we know that the area of a square is given by,

⇒ Area of square = side × side

⇒ (2x + 5)² = (side)²

⇒ side = √(2x + 5)²

⇒ side = 2x + 5 units.

Hence the expression which represents side of the square is 2x + 5 units.