What is the perimeter of the triangle? units

Mathematics

1 answer:

skelet666 [1.2K]3 years ago

8 0

Answer:

Perimeter = 30

Step-by-step explanation:

hypotenuse = $\sqrt{5^2+12^2}$

hypotenuse = $\sqrt{25+144}$

hypotenuse = $\sqrt{169}$

hypotenuse = 13

Perimeter = 5+12+13

Perimeter = 30

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Answer:

$y = 6 \sqrt{3} \: units$

Step-by-step explanation:

In order to find the value of y, first we need to find the length of the perpendicular dropped from one of the vertices of the triangle to its opposite side.

By geometric mean theorem:

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Next, by Pythagoras theorem:

${y}^{2} = {9}^{2} + {( \sqrt{27} )}^{2} \\ \\ {y}^{2} = 81 + 27 \\ \\ {y}^{2} = 108 \\ \\ y = \sqrt{108} \\ \\ y = \sqrt{36 \times 3} \\ \\ y = \sqrt{ {6}^{2} \times 3} \\ \\ y = 6 \sqrt{3} \: units$