Answer: x = 64
Step-by-step explanation:
First, order each of the three right triangles by the lengths of the sides. Each triangle has a small (s) leg, a medium (m) leg, and a hypotenuse (h). You can determine their order visually.
Left Δ: s = 36 m = unknown h = 60
Right Δ: s = unknown m = x h = unknown
Big Δ: s = 60 m = unknown h = 36 + x
Next, notice that you can set up a proportion with the Left and Big triangles using the s and h. We can't use m because it has two unknowns.
[tex]\dfrac{s}{h}:\quad \dfrac{36}{60}=\dfrac{60}{36+x}[/tex]
Cross multiply and solve for x:
36(36 + x) = 60(60)
1296 + 36x = 3600
36x = 2304
x = 64
