Question

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

Answer 1

The sum of the lengths of two legs of the 30°-60°-90° right triangle is 6.69 centimeters. Using the ratio of sides for the 30°-60°-90° triangle, the sum is calculated.

What is the ratio of sides for the 30°-60°-90° triangle?

The ratio for the 30°-60°-90° triangle is 1:√3:2 or x:x√3:2x

where x corresponds to the length opposite the 30° angle and x√3 is opposite of the 60° angle and 2x is opposite to the 90° angle.

Calculation:

It is given that the triangle is a right triangle with angles 30°-60°-90°

For such a triangle, the ratio of side lengths is x: x$\sqrt{3}$:2x

we have the length of the hypotenuse is $2\sqrt{6}$

So, 2x = $2\sqrt{6}$

⇒ x = $\sqrt{6}$

So,

the other length of the other leg is x√3 = √6 × √3 = 3 √2

Then, the sum of these two legs = √6 + 3√2 = 6.69 centimeters.

Learn more about the ratio of sides of a 30°-60°-90° triangle here:

https://brainly.com/question/6695000

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