A 2 inch by 2 inch square has its area increased by 21 square inches producing a new square. How many inches long is a side of the new square?
I think that the answer would be 5 because it is √25.
the answer is 5
thank you and I appreciate the help with my math homework
To find the length of a side of the new square, we need to determine how much the length of the side of the original square increased.
Let's define "x" as the increase in length for each side of the square. Since the original square has sides measuring 2 inches, the new square will have sides measuring (2 + x) inches.
Now, we are given that the area of the new square is increased by 21 square inches. Since the area of a square is calculated by multiplying the length of its side by itself, we can set up the equation:
(2 + x)^2 - 2^2 = 21
Expanding and simplifying the equation:
(4 + 4x + x^2) - 4 = 21
Simplifying further:
4x + x^2 = 21
Rearranging the equation to a quadratic form:
x^2 + 4x - 21 = 0
Now, to find the value of "x" that satisfies this equation, we can factor or use the quadratic formula.
Factoring the equation:
(x - 3)(x + 7) = 0
From this, we can see that x = 3 or x = -7. Since we are dealing with a physical length, the negative value is not applicable in this context. Therefore, x = 3.
Finally, we can calculate the length of a side of the new square by adding the increase to the original length:
2 inches + 3 inches = 5 inches
Therefore, the new square has sides that measure 5 inches in length.
new square:
(x+2)(x+2)
(x+2)^2 - 4 = 21
x^2 + 4x +4 - 4 - 21 = 0
x^2 + 4x - 21 = 0
(x+7)(x-3) = 0
x = -7 or x = 3, x = -7 making no sense
new square = 2+3 or 5 units long
check:
old square = 2x2 = 4
new square = 5x5 = 25
increase is 25-4 = 21 , as given
All is good