Question

How do you solve this problem??​

Answer 1

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.

$\dfrac{s}{h}:\quad \dfrac{36}{60}=\dfrac{60}{36+x}$

Cross multiply and solve for x:

36(36 + x) = 60(60)

1296 + 36x = 3600

           36x = 2304

               x = 64