Mathcount 21-30

Right triangle QRS, shown here, has altitude ST. If QR = 26 cm and

QT:RT = 9:4, what is the length of ST in cm?

(a)  

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CCSS.HSG.CO.C.10

In isosceles triangle WXY, shown here, WX = WY = 5 cm and XY = 8 cm.

What is the length of the altitude drawn perpendicular to side XY in cm?

(a)  

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CCSS.HSG.CO.C.9

What is the arithmetic mean of the altitude lengths of an isosceles triangle with two sides of length

13 cm and one side of length 10 cm? Express your answer as a common fraction.

(a)  

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CCSS.HSG.CO.C.10

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CCSS.HSG.CO.C.10

Triangle ABC has medians AD, BE and CF with centroid G. If AG = 6x and DG = 5x − 8, what is

the value of x?

(a)  

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CCSS.HSG.CO.C.10

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CCSS.HSG.CO.C.10

Triangle PQR has angle bisector PS, as shown, with PQ = 16 cm, RS = 11 cm

and QS = 8 cm. What is the perimeter of triangle PQR?

(a)  

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CCSS.HSG.CO.C.9

Triangle ABC has angle bisectors AD, BE and CF, as shown, and AB = 10,

BC = 7, AC = 11. What is the ratio of DG to AG? Express your answer as a

common fraction.

(a)  

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CCSS.HSG.C.A.3

The figure shows an inscribed circle tangent to triangle ABC at points D,

E and F on sides AB, BC and AC, respectively. If AB = 15 cm, BC = 14 cm

and BD = 6 cm, what is AC in cm?

(a)  

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CCSS.HSG.C.A.3