Question

(50 POINTS!!) The area of a square, in square units, is $38$ more than $10$ times the length of a side of the square, in units.

Find all possible values for the side length of the square.

Answer 1

Explanation:

Area of a square = s x s and this equals 10 x s

this is :

s^2 = 10 s divide both sides of the equation by 's'

s = 10 units ( or zero....but that makes no sense)

Answer 2

The area of a square, in square units, is $38$ more than $10$ times the length of a side of the square, in units, the approximate value of the side length to be 12.39 units.

To solve this problem, let's represent the side length of the square as 'x'.

According to the given information, the area of the square is 38 more than 10 times its side length, so we can set up the equation: x^2 = 10x + 38.

To solve this quadratic equation, let's rearrange it and set it equal to zero: x² - 10x - 38 = 0.

Now, we can either factor this equation or use the quadratic formula to find the values of 'x'.

In this case, let's use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a), where a = 1, b = -10, and c = -38.

After solving the equation, we find that the possible values for the side length of the square are approximately 12.39 and -2.39.

However, since we cannot have a negative side length, so therefore the only valid value is approximately 12.39 units.