The coordinates of two of the vertices of square QRST are shown.

Q (3.6,2.1)

R (¯5.4,2.1)

What is the length, in units, of each side of square QRST? Use the coordinates to show or explain how you determined the length.

Enter your answer and your work or explanation in the space provided.

Therefore the length of each side of square is .

Step-by-step explanation:

Given that,

                is a square.

                The coordinate of point is .

                The coordinate of point is .

Let, The coordinate of point is and the coordinate of point is .

Diagram of the square is shown below:

Now,

                         [Distance Formula]

Therefore the length of square is

                    [, because is a square]

⇒

squaring both sides, we get

⇒

⇒ ±

∴

The coordinate of point is and the coordinate of point is .

∵ is a square

∴  

Therefore the length of each side of square is .

step-by-step explanation:

try remembering the steps

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)