Solution Found!
Rectangles in triangles Find the dimensions and area of
Chapter 7, Problem 46E(choose chapter or problem)
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 \(90^{\circ}\).)
Questions & Answers
QUESTION:
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 \(90^{\circ}\).)
ANSWER: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.