Answer:
x = 2.4
I'm not sure how the answer is 4.5 but I'm pretty sure this is right unless I'm missing something
Explanation:
So we need to find how much shorter is the short line compared to the longer one. Basically we need a scale factor, for this we can use the side lengths already given to us, 10 and 15. So u can choose either enlarge the short line or shorten the longer one.
If u want to enlarge the short line then do 15/10 which is 3/2 which u will then multiply the shorter line's equation with it, if u want to shorten the longer line then do 10/15 which is 2/3 and multiply the longer lines equation with it.
I'll be using the 3/2 one cause why not:
3/2(x + 6) = 4x + 3
3/2x + 18/2 = 4x + 3
multiply the entire equation with 2 to make 3/2 no longer a fraction
(3/2x + 18/2 = 4x + 3)2
6/2x + 18 = 8x + 6
3x + 18 = 8x + 6
subtract 18 from both sides
3x = 8x - 12
subtract 8x from both sides
-5x = - 12
divide -5 from both sides
x = 2.4
U can input x into the equation to check:
3/2(2.4 + 6) = 4(2.4) + 3
12.6 = 12.6, it's right