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vagabundo [1.1K]
3 years ago
12

Find the unknown side length, x. Write your answer in simplest radical form.

Mathematics
2 answers:
Lana71 [14]3 years ago
4 0
I hope this helps you

Hitman42 [59]3 years ago
4 0

Answer:

x=4

Step-by-step explanation:

It is given that LMN is a right angled triangle which is right angled at M, therefore using the Pythagoras theorem, we have

(NL)^{2}=(MN)^{2}+(ML)^{2}

Substituting the given values, we get

(\sqrt{20})^{2}=(x-2)^{2}+x^{2}

20=x^2+4-4x+x^2

20=2x^2-4x+4

2x^2-4x-16=0

x^2-2x-8=0

x^2-4x+2x-8=0

x(x-4)+2(x-4)=0

(x+2)(x-4)=0

Thus, the value of x will be equal to 4 because x cannot take the negative value.

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