Rectangles in triangles Find the dimensions and area of the rectangle of maximum area that can be inscribed in the following figures. a. A right triangle with a given hypotenuse length ?L b. An equilateral triangle with a given side length ?L c. A right triangle with a given area ?A d. An arbitrary triangle with? a given area ?A (The result applies to any triangle, but first consider triangles for which all the angles are less than or equal to 90°.)
Solution 46E Step 1 (a onsider a right triangle with a hypotenuse le ngth . Find the dimension and area of the rectangle of maximum area that can be inscribed into it Draw a rectangle inside a right angled triangle with the hypotenuse length . The length of the re tangle i and width is y.