Answer:
x=5 so x+1 = 6 and x+3 = 8
Step-by-step explanation:
It's all about proportions. These are similar triangles, so corresponding sides are proportional. Basically you want to solve an equation
Let me know if you cannot see how EG corresponds to GH or how EF corresponds to IH.
Anyway, from here we just solve. Again, let me know if you have any questions.
4(x + 1) = 3(x + 3)
4x + 4 = 3x + 9
x = 5
And you can check
[tex]\frac{6}{8} = \frac{3}{4}[/tex
Given
we have
Squaring both sides, we have
And finally
Note that, when we square both sides, we have to assume that
because we're assuming that this fraction equals a square root, which is positive.
So, if that fraction is positive you'll actually have roots: choose
and you'll have
Which is a valid solution. If, instead, the fraction is negative, you'll have extraneous roots: choose
and you'll have
Squaring both sides (and here's the mistake!!) you'd have
which is not a solution for the equation, if we plug it in we have
Which is clearly false