Find max area of rectangle inside a right triangle.

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Homework Help Overview

The problem involves finding the area of the largest rectangle that can be inscribed in a right triangle with specified leg lengths. The rectangle's sides are aligned with the triangle's legs.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the dimensions of the rectangle and the triangle, particularly through the use of similar triangles to derive equations. There is a focus on understanding the ratio that connects the rectangle's dimensions.

Discussion Status

The discussion is ongoing, with participants exploring the derivation of an equation relating the rectangle's dimensions. Some guidance has been offered regarding solving the ratio equation for one variable and substituting it into the area expression.

Contextual Notes

There are indications of confusion regarding the presentation of information, particularly with visual aids, which may affect understanding. The original poster's approach to deriving the relationship between dimensions is under scrutiny.

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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