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# help geometry

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+4617

What is the sum of the lengths, in centimeters, of the two legs of a 30-60-90 right triangle, if the length of the hypotenuse is $$2\sqrt{6}$$ centimeters?

Apr 26, 2018

#1
+118626
+4

Draw an equilateral triangle of side length 2

now split it down the middle to form two congruent right angled triangles.

The angles on these 2 triangles are 90,60, and 30 degrees

the side lengths are  2,1 and sqrt3   (gained using Pythagoras's theorum)

The the hypotenuse of a similar triangle is 2root6 then that is a dilation of root6

2*sqrt6 = 2sqrt6

1*sqrt6 = sqrt6

sqrt3*sqrt6 = sqrt18 = 3sqrt2

Perimeter is

$$2\sqrt6+\sqrt6+3\sqrt2\\ =3\sqrt6+3\sqrt2\;\;cm$$

Apr 26, 2018

#1
+118626
+4

Draw an equilateral triangle of side length 2

now split it down the middle to form two congruent right angled triangles.

The angles on these 2 triangles are 90,60, and 30 degrees

the side lengths are  2,1 and sqrt3   (gained using Pythagoras's theorum)

The the hypotenuse of a similar triangle is 2root6 then that is a dilation of root6

2*sqrt6 = 2sqrt6

1*sqrt6 = sqrt6

sqrt3*sqrt6 = sqrt18 = 3sqrt2

Perimeter is

$$2\sqrt6+\sqrt6+3\sqrt2\\ =3\sqrt6+3\sqrt2\;\;cm$$

Melody Apr 26, 2018
#2
+4617
+3

Thank you so much, Melody!

tertre  Apr 26, 2018