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avatar+564 

I attempted this problem but Im completely lost. 

 

 Mar 7, 2016

Best Answer 

 #3
avatar+102396 
+5

By the Pythagorean Theorem, we have

 

c = √ [8^2 + 6^2]  = √100  = 10

 

And by similar triangles, we have

 

8 / 6   = [ a + 8 ] / 9       cross-multiply

 

72  = 6 [a + 8 ]

 

72  = 6a + 48    subtract 48 from both sides

 

24  = 6a    divide both sides by 6

 

4 = a

 

And by similar triangles, again, we have

 

8 / c   = [ a + 8 ]  /  [ b + c ]

 

8 / 10  = [ 4 + 8 ] / [ b + 10]   

 

4 / 5  = [ 12 ] / [ b + 10 ]      cross-multiply

 

4 [ b + 10 ] = 12 * 5

 

4b + 40  = 60    subtract 40 from both sides

 

4b  = 20      divide both sides by 4

 

b = 5

 

 

 

cool cool cool

 Mar 7, 2016
 #1
avatar+5259 
+4

It looks like similarity in right triangles... 

 Mar 7, 2016
 #2
avatar
+5

a=4

c=10

b=5

 Mar 7, 2016
 #3
avatar+102396 
+5
Best Answer

By the Pythagorean Theorem, we have

 

c = √ [8^2 + 6^2]  = √100  = 10

 

And by similar triangles, we have

 

8 / 6   = [ a + 8 ] / 9       cross-multiply

 

72  = 6 [a + 8 ]

 

72  = 6a + 48    subtract 48 from both sides

 

24  = 6a    divide both sides by 6

 

4 = a

 

And by similar triangles, again, we have

 

8 / c   = [ a + 8 ]  /  [ b + c ]

 

8 / 10  = [ 4 + 8 ] / [ b + 10]   

 

4 / 5  = [ 12 ] / [ b + 10 ]      cross-multiply

 

4 [ b + 10 ] = 12 * 5

 

4b + 40  = 60    subtract 40 from both sides

 

4b  = 20      divide both sides by 4

 

b = 5

 

 

 

cool cool cool

CPhill Mar 7, 2016

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