Which diagram shows the medians of a triangle?

a.
triangle 1
b.
triangle 2
c.
triangle 3
d.
triangle 4

For this case we have that, by definition, the medians of a triangle are the line segments that are drawn from a vertex to the midpoint of the opposite side of the vertex. The medians of a triangle are concurrent at a point.

If we look at the figure, we can discard triangles 3 and 4.

Also, by definition, the median divides the vertex angle into two equal angles.

Thus, the correct option is triangle 1.

Triangle 1

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)