Angie has a square dog pen with a perimeter of 20 meters. She wants to put a diagonal piece of fencing inside her pen to cut it in half because her 2 dogs have been fighting. How long of a piece of fencing will she need to buy? Hint: The formula for finding the hypotenuse of a right triangle is: a² + b² = c²

7.07 miles

Step-by-step explanation:

Hi, to answer this, first, we have to find the length of the square dog pen.

Perimeter of a square = 4 x sides

Replacing with the value given:

20 = 4 s

Solving for s:

20/4=s

Side = 5 meters

Since the situation forms a right triangle (see attachment) we have to apply the Pythagorean Theorem:  

c^2 = a^2 + b^2  

Where c is the hypotenuse of the triangle (in this case length of the diagonal) and a and b are the other sides.  

Replacing with the values given:  

c^2 = 5^2 + 5^2  

c^2 = 25+25

c^2 = 50

c = √50

c = 7.07 miles  

Feel free to ask for more if needed or if you did not understand something.  

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .