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In triangle \($XYZ$, $\angle X = 60^\circ$ \) and \($\angle Y = 45^\circ$.\)  Point  D lies on YZ such that DX bisects angle DXY. If  XD=24 then find the area of triangle XYZ.

 

 

A square is inscribed in a right triangle, as shown below. The legs of the triangle are 2 and 3. Find the side length of the square.

 

[asy]
unitsize(1.5 cm);

pair A, B, C, D, E, F, G;

A = (0,0);
C = (5,0);
B = (3^2/5,3*4/5);
D = extension(B, A + (0,-5), A, C);
G = extension(B, C + (0,-5), A, C);
E = extension(D, D + (0,1), A, B);
F = extension(G, G + (0,1), B, C);

draw(A--B--C--cycle);
draw(D--E--F--G);
[/asy]

 

 

 

Thank you so much!!! :)
 

 May 14, 2020
 #1
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-1

I can't understand what the problem is asking.

 May 14, 2020
 #2
avatar+179 
+2

 

Which one? Or both. If you want you can answer one, you do not need to answer both. You don't have to answer at all if you do not want ! :)

Noori  May 15, 2020

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