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Two of the altitudes of an acute triangle divide the sides into segments of lengths 5,3,2 and x units, as shown. What is the value of x?

 

 Nov 19, 2020
 #1
avatar+1062 
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Two of the altitudes of an acute triangle divide the sides into segments of lengths 5,3,2 and x units, as shown. What is the value of x?

 

x = 18

 

 Nov 20, 2020
 #2
avatar+116125 
+1

Call the apex angle  A

The  left base angle B

The right base angle C

Let the altitude meeting base (3 + 5)  =  8  be DC

Let the altitude meeting base 2 + x  be EB

 

Note  that right   triangles  AEB   and   ADC are similar

 

This implies that    AB/ AE  =  AC/ AD 

 

So

 

8 / 2 = (2 + x) /  5      

 

4  = (2 + x)  / 5

 

5*4  = 2 + x

 

x = 5*4  - 2

 

x   = 18    ( just as  jugoslav found  !!! )

 

cool cool cool

 Nov 20, 2020

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