Find the dimensions of the rectangle of maximum area that can be inscribed in a right triangle with base 6 units and height 4 units?
1 Answer
Rectangle will be
Explanation:
Consider the area of the enclosing triangle, since it is a right triangle it's area is given by
Let the area of the rectangle =
Consider the two small triangles left over by the intrusion of the rectangle.
The one lying on the
The one on the
So the total area of the triangle =
Multiplying both sides by
We can now differentiate this with respect to the area A. [since we have the variables in terms of of
Substituting this value of
Sorry I am unable to include a sketch, getting on a bit now and technology has left me behind somewhat.