10, because then meg would have 5.
SA= Lateral Area + Area (of base)
Lateral area = perimeter of base x height
An isosceles triangle has two congruent base segments. The hypotenuse of an isosceles right triangle is (length of base segment) x (the square root of 2). I did the math for you (shown above) to get 5 as a base.
So 5 + 5 + square root of 50 is your perimeter
Multiply the perimeter times your height (8) and you get the lateral area.
Add your lateral area to the base area (triangle = 1/2 bh)
LA = 136.568...
Area of Triangle base = 12.5
Surface area = 149.068... square cm
It is a similar triangle so the side length of the smaller triangle (x and x-2) are in the same ratio as the bigger triangle (2x+5 and 2x-1). As the ratio is the same, you can equate them and solve for x.
Either or can be used with any triangle...I personally find the law of sines is often more compact as in this case we can just say;
(sin115)/18=(sin40)/c (with no need for b or B as would be needed with the law of cosines...)
c=18(sin40)/(sin115)
c≈12.77