Question 1147732: The sides of a triangle are 14 cm, 48 cm, and 50 cm. What is the perpendicular distance from the longest side to the midpoint of the shortest side, in cm?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52754)   (Show Source):
You can put this solution on YOUR website! .
1) Use the Heron's formula to calculate the area "A" of the given triangle.
2) Then find the altitude "h" of the triangle drawn to the longest side, from the equation
A =  .
3) Then one half of the "h" will be your answer.
Answer by greenestamps(13195)  (Show Source):
You can put this solution on YOUR website!
Let the triangle be ABC, with AB=14, BC=48, and CA=50. Those side lengths are a Pythagorean Triple; the triangle is a right triangle.
Let M be the midpoint of AB and let N be the midpoint of CA. Then Triangles ABC and AMN are similar, in the ratio 2:1. So triangle AMN has side lengths 7, 24, and 25.
We are to find the length of MP, where P is the point on CA for which MP is perpendicular to CA.
The area of triangle AMN, using AM and MN as the base and height, is (1/2)(7)(24) = 84.
The area of the same triangle, using AN and MP as the base and height, is (1/2)(25)(MP).
So
ANSWER: The perpendicular distance from the longest side to the midpoint of the shortest side is 168/25 cm, or 6.72cm.
|
|
|
