The value of n is 12. and m is 6root5
We have given the diagram,
The measurement of m,
n = 12
According to the altitude theorem
What is the altitude theorem?
The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two-line segments it creates on the hypotenuse.
24/n = n/6
The Cross multiply
24 * 6 = n²
144 = n²
n² = 144
n = √144
n = 12
[tex]m^2=6^2+n^2[/tex]
[tex]m^2=6^2+12^2\\m^2=36+144\\m^2=180[/tex]
[tex]m=\sqrt{180} \\m=2\cdot \:3\sqrt{5}\\m=6\sqrt{5}[/tex]
Hence the value of n is 12.
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