Question 1134890: PLs pls pls i am dying here alone pls help me out with this question
if a rectangle of the greatest possible area is inscribed in a triangle whose base is 'b' and altitude 'h' then determine the area of the rectangle
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! the maximum rectangle area occurs when the midpoints of two of the sides of the triangle are joined to make a side of the rectangle and its area is half of the area of the triangle
:
The area of the triangle is bh/2
:
The length of the rectangle is b/2 and the width of the rectangle is h/2 where b is the triangle's base and h is the triangle's height
:
Maximum area rectangle is b/2 * h/2 = bh/4 or 1/2 the area of the triangle
:
You can visualize this by connecting the midpoints of the two sides of the triangle(this forms a length of the rectangle, the other length lies on the base of the triangle), the two widths of the rectangle are formed by connecting the midpoints of the two sides of the triangle to the triangle's base with lines that are perpendicular at the base of the triangle.
:
Now flip the three triangles into the rectangle, they cover the rectangle and represent half the area of the triangle.
:
|
|
|
