Question

Find the value of each variable for the right triangles. Make sure all answers are in reduced radical from. Shoe your work.

Answer 1

Denote each of the triangles ABC, where B is the right angle.

a.


`t^(2)+ 12^(2)= 13^(2)`

instead of taking the square of 12 and 13, , take 12 squared to the right side and apply the difference of squares formula:
`a^(2)- b^(2)=(a-b)(a+b)`


`t^(2)= 13^(2)- 12^(2)=(13-12)(13+12)=1*25`

so t is square root of 25, which is 5

b.


`a^(2)+9 ^(2) = 12^(2)`


`a^(2)= 12^(2) -9 ^(2)=(12-9)(12+9)=3*21=3*3*7`


`a= √(3*3*7)=3 √(7)`


b.


`6^(2) + 9^(2) = x^(2)`


`36+81= x^(2)`

here we can factorize 9, to work with small numbers:


`9(4+9)= x^(2)`


`9*13= x^(2)`


`x^(2) =3*3*13`


`x= √(3*3*13)=3 √(13)`