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Two right triangles share a side as follows. What is the area of triangle ACE?

 

 Dec 17, 2021
 #1
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The area of triangle ACE is 30.

 Dec 17, 2021
 #2
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I'm still trying to figure it out,  

but I know answer #1 isn't correct. 

 

ACE is part of ACB.  

Area of ACB is 24.  

How can a part be more than the whole?  

.

Guest Dec 17, 2021
 #3
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[ACE] = 13.71428571 square units

 Dec 17, 2021
 #4
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For triangle CEA, let height from CA to E be h1

For triangle DEB, let height from DB to E be h2

h1 + h2 = 6, ratio of CA/DB = 8/6 = 4/3 ie h1 = 4/3(h2)

h1 + h2 = 6 => 4/3(h2) + h2 = 7/3h2 = 6 => h2 = 18/7, h1 = 24/7

Area of ACE = (1/2)(8(24/7) = 48/7 sq units

 Dec 17, 2021
 #6
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For triangle CEA, let height from CA to E be h1

For triangle DEB, let height from DB to E be h2

h1 + h2 = 6, ratio of CA/DB = 8/6 = 4/3 ie h1 = 4/3(h2)

h1 + h2 = 6 => 4/3(h2) + h2 = 7/3h2 = 6 => h2 = 18/7, h1 = 24/7

Area of ACE = (1/2)(8(24/7) = 96/7 sq units

Guest Dec 17, 2021
 #5
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0

For triangle CEA, let height from CA to E be h1

For triangle DEB, let height from DB to E be h2

h1 + h2 = 6, ratio of CA/DB = 8/6 = 4/3 ie h1 = 4/3(h2)

h1 + h2 = 6 => 4/3(h2) + h2 = 7/3h2 = 6 => h2 = 18/7, h1 = 24/7

Area of ACE = (1/2)(8(24/7) = 192/14 = 96/7 = 13.71 sq units

 Dec 17, 2021

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