The width and height of the rectangle inscribed in the right triangle have a measure of 3.529 units.
How to find the dimensions of the rectangle of maximum area by optimization
In this problem we must use critical values and algebraic methods to determine to determine the dimensions of the rectangle such that the area is a maximum. The equation of the quadrilateral is formed by definition of the area of a rectangle:
A = w · h (1)
Where:
- w - Width of the rectangle.
- h - Height of the rectangle.
And the area of the entire triangle is:
0.5 · (5) · (12) = w · h + 0.5 · w · (12 - h) + 0.5 · (5 - w) · h
30 = w · h + 6 · w - 0.5 · w · h + 2.5 · h - 0.5 · w · h
30 = 6 · w + 2.5 · h
2.5 · h = 30 - 6 · w
h = 12 - 2.4 · w (2)
The quadrilateral of maximum area is always a square, then we must solve for w = h:
w = 12 - 2.4 · w
3.4 · w = 12
w = 3.529
Then, the width and height of the rectangle inscribed in the right triangle have a measure of 3.529 units.
To learn more on optimizations: https://brainly.com/question/15319802
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