SOLUTION: Given: ΔTSP, TS = SP = 10cm, TP = 12cm. Find: Three altitudes of ΔTSP.
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Question 1064313: Given: ΔTSP, TS = SP = 10cm, TP = 12cm. Find: Three altitudes of ΔTSP.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Let M be the point on TP where the bisector of angle TSP intersects TP
:
Since triangle TSP is isosceles, SM is the perpendicular bisector of TP
:
By Pythagorean Theorem,
:
6^2 + SM^2 = 10^2
:
SM^2 = 10^2 - 6^2 = 100 - 36 = 64
:
SM = 8 cm
:
Area(A) of triangle TSP = (1/2) * 12 * 8 = 48 cm^2
:
now we can use area 48 cm^2 to solve for the other two altitudes
:
48 = (1/2) * 10 * h
:
5h = 48
:
h = 9.6
:
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The three altitudes are 9.6 cm, 9.6 cm, 8 cm
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:
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