What is the length of the Midsegment?
12
18
6
9

The length of Midsegment = 9

Step-by-step explanation:

the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side.

According to the Midsegment Theorem:

Thus,

The midsegment (x+4) is half the length of the third side (4x-2). so

Subtract 4 from both sides

Subtract 2x from both sides

Simplify

divide both sides by -1

Simplify

As

The length of Midsegment = x+4

                                             = (5) + 4        ∵ x = 5

                                             = 9

Therefore, the length of Midsegment = 9

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)