Answer:
x = +2√21 and y = +2√30
Explanation:
The two marked sides of the smaller triangle are x and y. The third side has length equal to 14 - 8, or 6.
We can thus write two equations in x and y:
x^2 = y^2 + 6^2
and
y 6
-- = ---
8 y
Solving the first equation for y^2 yields y^2 = 36 - x^2. Solving the second equation for y^2 yields 48. Thus 36 - x^2 = 48, and
x^2 = 84. Thus, x = +√7*√4*√3, or x = +2√21.
We now find y. y^2 = 36 = x^2, which here becomes
y^2 = 36 + 4(21) = 36 + 84 = 120. Thus, y = +√4*√30, or y = +2√30.