An acute triangle has side lengths 21 cm, x cm, and 2x cm. If 21 is one of the shorter sides of the triangle, what is the greatest possible length of the longest side, rounded to the nearest tenth?
Joey is building a frame for a sandbox. The sandbox is going to be a quadrilateral that has the lengths shown.

Point Z is the incenter of ΔSRT.

Which must be true? Select two options.



Triangle L N P has centroid S. Lines are drawn from each point to the midpoint of the opposite side to form line segments N R, L P, and Q M. The length of line segment N S is 7 x minus 3 and the length of line segment S R is 5 x minus 3.

In which figure is point G a centroid?




Point X is the circumcenter of ΔABC.What is the length of XB?

The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth.
Point Z is the circumcenter of ΔLMN.





Which classification best represents a triangle with side lengths 10 in., 12 in., and 15 in.?
Triangle A B C is shown. Lines are drawn from each point to the opposite side and intersect at point D. They form line segments A G, B E, and C F.

Triangle T R S has centroid Z. Lines are drawn from each point to the midpoint of the opposite side to form line segments T W, R V, and S U.

In the diagram, Z is the circumcenter of triangle TUV.

In triangle TRS, TZ = (3x) inches and WZ = (2x - 3) inches.[Figure may not be drawn to scale]

In triangle ABC, EG = x inches and BG = (5x - 12) inches. [Figure may not be drawn to scale]

Point H is the circumcenter of ΔJKL.





Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?
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