Question

Find the length of the third side. Write is simplest radical form show work.

Answer 1

`\longmapsto \: 9^2+b^2 = (\sqrt(97))^2`

`\longmapsto \: 81+b^2=97`

`\longmapsto \: b^2 = 97-81`

`\longmapsto \: b^2 = 16`

`\longmapsto \: b = 4`

Answer 2

4

Explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

9^2 + b^2 = (sqrt(97) )^2

81 + b^2 = 97

Subtract 81 from each side

b^2 = 97-81

b^2 = 16

Take the square root of each side

sqrt(b^2) = sqrt(16)

b = 4