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A square with side length 4 is placed against a square with side length a.  The area of the red region is 88/15.  Find a.

 

 Dec 11, 2020
 #1
avatar+114221 
0

The area of  one of the  right triangular white regions in the smaller square is

 

(4^2 - 88/15)/2  =  76/15

 

So......the other leg , L,  of  one of these right triangles can be found as

 

76/15 =  (1/2) 4 *  L

 

76/30  = L  =  38/15

 

So   the top side of the red region  has the length  =   4 - 38/15 =   [60 -38]/15 = 22/15

 

And using similar triangles  the difference, D, in height between the larger square and the smaller square is

 

4/(38/15)  =  D/ ( 22/15)

 

4/38 =  D/22

 

88 = 38D

 

88/38 = D

 

44/19 =   D

 

a  =  4  + 44/19  =    [76 + 44 ]  /19  =  120/19

 

cool cool cool

 Dec 11, 2020
 #2
avatar+846 
0

I think that your answer is not correct.

 

According to your calculations is as follows:

 

4 * tan∠FBC = 6.315789474

 

6.315789474 / tan∠EBD = 9.972299169     ( 4 + a )

 

AX and CZ are not congruent!!!

 

We need to look for the correct answer.

 

a = 6 units  smiley

 

 

 

jugoslav  Dec 12, 2020
edited by jugoslav  Dec 12, 2020
edited by jugoslav  Dec 12, 2020
edited by jugoslav  Dec 12, 2020
edited by jugoslav  Dec 12, 2020
edited by jugoslav  Dec 12, 2020
 #3
avatar+846 
0

I'll come back if I get the right answer. laugh

 

And the answer is     a = 6 units  smiley

jugoslav  Dec 12, 2020
edited by jugoslav  Dec 12, 2020
edited by jugoslav  Dec 12, 2020
edited by jugoslav  Dec 12, 2020
edited by jugoslav  Dec 12, 2020
edited by jugoslav  Dec 12, 2020

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