Question

Help Asap Please Before I Get In Trouble???

Answer 1

`n=4√(3)`

Explanation:

Let the only unmarked side of the triangle in the given figure be x. By the Pythagorean Theorem,
`12^2+n^2=x^2.` Mark this as equation 1.

By the Pythagorean Theorem also,
`x^2+m^2=(12+4)^2` or
`x^2+m^2=16^2.` Mark this as equation 2.

Substituting equation 1 to equation 2 results to

`(12^2+n^2)+m^2=16^2\\n^2+m^2=16^2-12^2\\n^2+m^2=112.`

Mark
`n^2+m^2=112` as equation 3.

Looking at the smallest triangle and using the Pythagorean Theorem, then

`n^2+4^2=m^2\\n^2-m^2=-4^2\\n^2-m^2=-16.`

Mark
`n^2-m^2=-16` as equation 4.

Adding equation 3 and equation 4 results in

`n^2+m^2+(n^2-m^2)=112+(-16)\\2n^2=96\\n^2=48\\n=√(48)\\n=√(16\cdot3)\\n=4√(3).`

Hence, the value of n is
`n=4√(3).`