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2 years ago

What is the length of YZ in XYZ

Mathematics

1 answer:

Studentka2010 [4]2 years ago

3 0

AZ=12 - is hypotenuse

∠XZY=30° ⇒

$XY=\dfrac{1}{2} \times12=6$

$\text{By the Pythagorean theorem}\\YZ=\sqrt{12^2-6^2} =\sqrt{(12-6)(12+6)} =\sqrt{6\times18} =\sqrt{108} =6\sqrt{3}$

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$\overline{KN}\cong \overline{NM}\\ \\\overline{KL}\cong \overline{LM}\ [\text{option D is true}]$

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$\overline{KN}\cong \overline{NM},$

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$7x-4=5x+12\\ \\7x-5x=12+4\\ \\2x=16\\ \\x=8\ [\text{option A is true}]\\ \\MN=KN=7\cdot 8-4=56-4=52\ [\text{option C is true}]$

Option B is false, because KN=52 units.

Option E is false, because LN is congruent KN, not LM

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