To express: The length of the altitude which is perpendicular to the hypotenuse as a function of the length of the hypotenuse if one of the legs of a right triangle is 4 cm.
The length of the altitude as function of the length of the hypotenuse is, .
The length of the one leg of a right angle triangle is 4 cm and the other length of the other leg is b cm.
Let the length of the hypotenuse is h cm and the length of the altitude which is perpendicular to the hypotenuse is ha cm.
Thus, by the Pythagoras theorem, .
This implies, .
Area of the triangle is .
Here, the base is hypotenuse h cm and the height is ha cm.
So, the area is, . (1)
If the base is 4 and the height is b, then the area is, . (2)
Compare the equations (1) and (2) and simplify,
The length of the altitude ha is to be expressed as a function of hypotenuse.
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