The segment joining the midpoints of sides pq and pr (the midsegment) in traingle pqr has length 8x^12x+36. if the length of qr is 4x^2+60x+120, find all possible measures of the midsegment

The possible measures of the midsegment are 32 units and 212 units.

Step-by-step explanation:

Given:

A triangle PQR with the midsegment made by sides PQ and PR has length equal to and the base length QR opposite to the midsegment is .

From midsegment theorem, we know that, the midsegment is a line parallel to the base opposite to it and half the length of the base length.

Therefore, Midsegment = Base length QR

Now, midsegment can be calculated using the values of 'x'.

First, plug in -1 for 'x'. This gives,

Now, plug in 4 for 'x'. This gives,

Therefore, the possible measures of the midsegment are 32 units and 212 units

in simplified version   it would be x ≤-4

step-by-step explanation:

multiply each term in x ≤-4 by -1

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.