The area of a square is 196cm2(squared), find the measure of one side. Thank you,, this is my assign. In math1, im using the formula A=s*s but i need to solve this using quadratic equation.
s^2 = 196
s = 14
check : 12 * 14 = 196
The side of a square that has an area of 196cm²
To find the measure of one side of a square given its area, you can use the formula A = s^2, where A represents the area of the square and s represents the length of one side of the square.
Given that the area of the square is 196 cm^2, we can set up the equation as follows:
196 = s^2
To solve for s using a quadratic equation, we can rearrange the equation into the quadratic form:
s^2 - 196 = 0
This equation can be solved by factoring or by using the quadratic formula. Here, let's demonstrate how to use the quadratic formula:
First, identify the coefficients of the quadratic equation:
a = 1 (coefficient of s^2)
b = 0 (coefficient of s)
c = -196 (constant term)
The quadratic formula is:
s = (-b ± √(b^2 - 4ac)) / 2a
Substituting the values into the quadratic formula, we get:
s = (0 ± √(0^2 - 4(1)(-196))) / 2(1)
Simplifying further:
s = (0 ± √(0 + 784)) / 2
s = (0 ± √784) / 2
Taking the square root of 784:
s = (0 ± 28) / 2
This gives us two possible solutions for s: s = 28/2 = 14 and s = -28/2 = -14. Since side lengths cannot be negative, we discard the negative solution.
Therefore, the measure of one side of the square is 14 cm.