Find max area of rectangle inside a right triangle.

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To find the area of the largest rectangle inscribed in a right triangle with legs of 5 cm and 12 cm, the relationship between the rectangle's dimensions and the triangle's sides is established through similar triangles. The solution involves deriving an equation that relates the rectangle's width (x) and height (y) using the triangle's proportions. By solving this ratio, one can express the area of the rectangle in terms of a single variable. The final step is to maximize this area expression to determine the dimensions that yield the largest rectangle. Understanding the geometric relationships is crucial for solving this problem effectively.
Brown Arrow
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Homework Statement


Find the area of the largest rectangle that can be inscribed in a right triangle with legs adjacent to the right angle of lengths 5cm and 12cm.
the two sides of the rectangle lie along the legs.


Homework Equations



N/a

The Attempt at a Solution



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Hi Brown Arrow! :smile:

(pleeeeeeease don't post such wide pictures! :redface:)
Brown Arrow said:
I don't get why he did the ratio …

he wanted an equation relating x and y, and he got it by comparing the two similar triangles :wink:
 
yea sorry about that could figure out how to shrink it :redface:
 
Now solve the ratio equation for x or y & plug the result into the expression for area.
 

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