Question

Solve for x.

6
4
X
6
1
x = [?]
Enter the number, in decimal form,
that belongs in the green box.

Answer 1

9514 1404 393

Answer:

x = 3.6

Explanation:

The angle bisector divides the segments proportionally. This means they satisfy ...

bottom segment / side segment = x/6 = (6-x)/4

Multiplying by 12 gives ...

2x = 3(6 -x)

2x = 18 -3x . . . . . eliminate parentheses

5x = 18 . . . . . . . . add 3x

x = 3.6 . . . . . . . . . divide by 5

_____

Alternate solution

I like to try to work these mentally. The total of side lengths is 10, so the total base length (6) is 6/10 = 0.6 times that. Then x will be 0.6 times the left side length: 0.6·6 = 3.6 = x.