AB + BC = AC x + 16 + 4x + 11 = 77
5x = 77 - 27
5x = 50
x = 50/5
x = 10
AB = x + 16
AB = 10 + 16
AB = 26

What is the reasoning for each step

Hey there mate :)

As per your question, AB + BC = AC are the sides of a triangle.

=> AB + BC = AC

( AC is hypotenuse and AB and BC are remaining two sides )

=> (x + 16) + (4x + 11) = 77

(These are the given values of each side such as [x+16]=AB ; BC=[4x+11] and AC=77)

=> 5x = 77 - 27

=> 5x = 50

=> x = 50/5

=> x = 10

( Now these above steps are the continuing solving processes of given values)

=> AB = x + 16

(Previously we got value x and now substitute its value)

=> AB = 10 + 16

=> AB = 26

(Now these are the remaining solving processes)

~ Benjemin360

it's both, now can you answer my most recent question?