SOLUTION: 10. If the sides of a triangle are 13, 14, and 15 cm long, then the altitude drawn to the 14-cm side is 12 cm long. How long are the other two altitudes? Which side has the longest
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Question 148446: 10. If the sides of a triangle are 13, 14, and 15 cm long, then the altitude drawn to the 14-cm side is 12 cm long. How long are the other two altitudes? Which side has the longest altitude?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First let's draw the picture.
From the drawing, we can see that the base is 14 cm and the height is 12 cm.
Note: the "base" can be any of the three sides.
Remember, the formula for the area of any triangle is
Plug in and
Multiply
Reduce
So the area of the triangle is 84 square cm
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Now, if we make the base any other side (let's say the side labelled "13 cm"), then the base becomes
Go back to the area of a triangle formula
Plug in and
Multiply.
Multiply both sides by 2.
Divide both sides by 13 to isolate "h".
So when the base is 13 cm, the height is 12.92308 cm
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Finally, if we make the base the last side, then the base is
Go back to the area of a triangle formula
Plug in and
Multiply.
Multiply both sides by 2.
Divide both sides by 15 to isolate "h".
So when the base is 15 cm, the height is 11.2 cm
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So the largest height is 12.92308 which occurs when the base is 13 cm
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