If the length of a diagonal square is 10 feet, the length of the side of the square is?

The side lengths is:

a = 5√2 or 7.07 units

Step-by-step explanation:

The diagram is attached below.

From the diagram, it is clear that we're dealing with a square, so all side lengths of the square would measure the same length.

Moreover, the angles B and D are right, thus we need to use the Pythagorean theorem to find the value of 'a'.

Here, a and b are the right containing sides

As a and b are equal, we consider them as 'a'.

Also, 'c' is the hypotenuse.

Hence,

The diagonal is the Hypotenuse  'c'.

so

a²+a² = 10²

2a² = 100

a² = 50

a = √50

a = 5√2             ∵√50=√25×2=5√2

a = 7.07 units

Therefore, the side lengths is:

a = 5√2 or 7.07 units

After 4 games cost to bowl will be the same at both bowling centers.

Step-by-step explanation:

Given:

ran in lanes charges

Per game charge = $2.5

rental charge for shoe = $2

Let the number of games played be 'x'.

So we can say that;

Total cost is equal to sum of Per game charge multiplied by number of games and rental charge for shoe.

framing in equation form we get;

Total cost =

fun time lanes

Per game charge = $2

rental charge for shoe = $4

So we can say that;

Total cost is equal to sum of Per game charge multiplied by number of games and rental charge for shoe.

framing in equation form we get;

Total cost =

To find the number of games when both cost would be same we have to make the total cost of both the bowling centers to be equal.

Hence we can say that;

=

Combining the like terms we get;

Dividing both side by 0.5 we get;

Hence After 4 games cost to bowl will be the same at both bowling centers.