Question

Hello there! Can I get someone help please ? Thanks!

Answer 1

Since they are right triangles use Pythagorean Theorem.
a^2 + b^2 = c^2 where c is the hypotenuse.

a.  12^2 + b^2 = 13^2
144 + b^2 = 169
subtract 144 from both sides
b^2 = 25
take the square root of both sides
t = 5  This is also know as a Pythagorean Triple 5-12-13

b.  a^2 + 9^2 = 12^2
     a^2 + 81 = 144
subtract 81 from both sides
a^2 = 63
take the square root of both sides
a = √63
a = √(9 * 7)
a = 3√7

c.   6^2 + 9^2 = c^2
    36 + 81 = c^2
117 = c^2
take the square root of each side
c = √117
c = √(9*13)
x = 3√13