Question

What is the value of k? k = ?

Answer 1

$m^2=4^2+8^2=16+64=80\\ m=\sqrt{80}=4\sqrt5\\\\\\ 4^2+k^2=l^2\\ l^2+(4\sqrt5)^2=(8+k)^2\\\\ k^2=l^2-16\\ l^2=64+16k+k^2-80=k^2+16k-16\\\\ k^2=k^2+16k-16-16\\ 16k=32\\ \boxed{k=2}$

Answer 2

From triangle LNO:

m² = 4² + 8²

m² = 16 + 64

m² = 80...............(a)

From triangle MNO

l² = k² + 4²

l² = k² + 16..........(b)

From triangle LNM

m² + l² = (k + 8)²        Recall: m² = 80,  (b)

80 + k² + 16 = k² + 16k + 64

k² - k² - 16k = 64 - 80 -16

-16k = -32

k = -32/-16

k = 2