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What is the value of y in the diagram below

 

 

A.7 square root 2

B.2 square root 3

C.square root 14

D.square root 5

 Jul 25, 2019
 #1
avatar+8718 
+3

 

m∠ABD  =  m∠CBA  because they are the same angle

m∠BDA  =  m∠BAC  because they are both right angles.

 

So by the AA similarity theorem, triangle ABD is similar to triangle CBA

 

Do you see what to do next?

 Jul 25, 2019
 #2
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+1

no i thought i did but then i got square root of 10 so no i don't get it still 

sorry can you explain it further plz 

Guest Jul 25, 2019
 #5
avatar+8718 
+3

Let's just look at the similarity statement  △ABD ~ △CBA

 

ABD ~ △CBA     AB  in the first triangle corresponds to  CB  in the second triangle.

 

△ABD ~ △CBA     BD  in the first triangle corresponds to  BA  in the second triangle.

 

So:

 

AB / CB  =  BD / BA

 

Do you see where that came from?

 

All that's left to do is plug in the lengths of those sides and solve for  y .

hectictar  Jul 25, 2019
 #6
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+1

wait it is square root 14 right i just got that 

Guest Jul 25, 2019
 #7
avatar+8718 
+4

Yep! That's what I got too smiley

hectictar  Jul 26, 2019
 #3
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+1

(5 +2) / y = y/2

7 / y = y / 2      cross myltiply

y^2 = 14

y = sqrt(14)

 Jul 25, 2019
 #4
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0

are yousure thats right or is 7 square root 2 

Guest Jul 25, 2019
 #8
avatar+103674 
0

sqrt (14) is not 7root 2

 

sqrt(98)= sqrt(49)*sqrt(2) = 7sqrt2

 Jul 26, 2019
 #9
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Tan ABC = y / (5+2) = Tan DBA = 2 / y
Or: y / 7 = 2 / y      Cross multiply
y^2 = 14
y = Sqrt(14)

 Jul 26, 2019

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