Question

Find the value of x. Round the answer to the nearest tenth, if needed.

A.
6.9
B.
15.9
C.
36.8
D.
42.3

Answer 1

let the other 2 unknown sides be y n z

look at the two smaller triangles inside

y^2 = 12^2 + x^2 and

z^2 = 21^2 + x^2

from the biggest triangle

(12+21)^2 = y^2 + z^2

substituting

(12+21)^2 = (12^2 + x^2) + (21^2 + x^2)

33^2 = 12^2 + 21^2 + 2x^2

2x^2 = (33^2 - 12^2 - 21^2)/2 = 504

x^2 = 252

x = 15.9

ans is B