joycelynandrews2006
joycelynandrews2006 joycelynandrews2006
  • 21-09-2022
  • Mathematics
contestada

What is the measure of m?
6
24
E
n
m = [?]√
Give your answer in simplest form.
Enter
PLEASE HELP ME

What is the measure of m 6 24 E n m Give your answer in simplest form Enter PLEASE HELP ME class=

Respuesta :

reinhard10158
reinhard10158 reinhard10158
  • 21-09-2022

Step-by-step explanation:

geometric mean theorem :

h = sqrt(p×q)

h being the height on the Hypotenuse in a right-angled triangle, p and q being the 2 line segments the height splits the Hypotenuse into.

so,

n = sqrt(6×24) = sqrt(144) = 12

m we get now via Pythagoras

m² = 6² + 12² = 36 + 144 = 180

m = sqrt(180) = sqrt(4×9×5) = 2×3×sqrt(5) = 6×sqrt(5)

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