Question #10a6c

1 Answer
Jan 18, 2018

See a solution process below:

Explanation:

The Pythagorean Theorem states:

#a^2 + b^2 = c^2#

Substituting the values from the problem gives:

#8^2 + (x - 1)^2 = (x + 3)^2#

#64 + (x^2 - 2x + 1) = (x^2 + 6x + 9)#

#64 + x^2 - 2x + 1 = x^2 + 6x + 9#

#64 + x^2 -color(red)(x^2) - 2x + color(blue)(2x) + 1 - color(green)(9) = x^2 -color(red)(x^2) + 6x + color(blue)(2x) + 9 - color(green)(9)#

#64 + 0 - 0 - 8 = 0 + (6 + color(blue)(2))x + 0#

#56 = 8x#

#56/color(red)(8) = (8x)/color(red)(8)#

#7 = (color(red)(cancel(color(black)(8)))x)/cancel(color(red)(8))#

#7 = x#

#x = 7#

The Solution Is:

#a = 8#

#b = x - 1 = 7 - 1 = 6#

#c = x + 3 = 7 + 3 = 10#

#8^2 + 6^2 = 10^2#

#64 + 36 = 100#

#100 = 100#