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The line x = k bisects the area of triangle ABC.  Find the value of k.

 

 Apr 19, 2022
 #1
avatar+115 
-4

You can use this app to help you it show an good example to help you math.stackexchange.com/questions/3486925/find-the-value-of-k-that-bisects-the-area 

let me know if you need any thing else have a great day 

 

 

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 Apr 19, 2022
edited by Kakashi  Apr 19, 2022
 #2
avatar+2455 
+1

The line \(x = k\) is a vertical line. It will split the triangle into a right triangle and a quadrilateral. 

 

The area of the triangle is \(10.5\)

 

The equation of line \(AB \) is \( {3 \over10}x+{9 \over5}\)

 

We want the area of the right triangle to be \(5.25\), so we can write the area as an equation: \(10.5=(x+6)({3 \over 10}x+{9 \over 5})\)

 

Solving the equation and simplifying, we find that \(\color{brown}\boxed{x = \sqrt{35} - 6}\)

 

Feel free to ask me if you have any questions!!

 Apr 19, 2022

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