MHB Find the value of X in terms of Y

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In the discussion, participants focus on finding the value of X in terms of Y using similar triangles. They establish that the ratio of the sides opposite equal angles is consistent, leading to the equation 7/Y = 9/X. This simplifies to 7Y = 9X, confirming the relationship. The final expression derived is X = 7Y/9. Additionally, a note is made about the importance of distinguishing between lowercase and uppercase letters in mathematical notation.
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mathlearn said:
All I see is the three angles of the triangles equal.
In this case the triangles are similar.
 
Evgeny.Makarov said:
In this case the triangles are similar.

As said above,

In similar triangles, the sides facing the equal angles are always in the same ratio

$\frac{7}{X}$ = $\frac{9}{Y}$

$7Y$ = $9X$

Correct I guess?

Many Thanks :)
 
mathlearn said:
$7Y$ = $9X$
Correct, but the final answer is $x=7y/9$ ("find the value of $x$ in terms of $y$").

Also, in mathematics lowercase and uppercase letters often denote different objects, so they should not be mixed.
 
Sure :) Thank you for the advice :)

Many Thanks :)
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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