Find the missing length indicated. Round to the nearest hundredth (two decimal places), if needed.

Question

Answer 1

easiest way to solve for x is to notice two similar triangles with sides

48/64 = x/48 =3/4, x/12=3 x=36

or do a more complicated tedious calculation

Let b = large triangle base, h= its height

then the bottom smaller triangle is a 3-4-5 triangle magnified by 12, 36-48-60

x =36

h^2 = 48^2 +64^2 =6400

h=80

h^2 + b^2 = (64+x)^2 = 4096 + 128x + x^2

6400+b^2 = 4096 +2x +x^2

b^2 = -2304 + 128x +x^2

b^2 =2304 +x^2 subtract to get

0= -4608+ 128x

128x =4608

x = 4608/128 = 36

this all assumes 64+x is the hypotenuse (and not 64 with x part of the 64?)