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?

tertre
Apr 26, 2018

#1**+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

#1**+4 **

Best Answer

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