Question

A right triangle has a leg with a length of 15 and a hypotenuse with a length of 15√2 Tameka believes it is a 45-45-90 triangle. Which of the following statements are correct? Select all that apply: A. The angle opposite to the side with length 15 measures 30 degrees B. Tameka is correct. It is a 45-45-90 triangleC. The measure of the remaining leg is 15√3 D. The measure of the remaining leg is also 15 E. The perimeter of the triangle is 45√2

Answer 1

If the triangle is a 45-45-90, then it must be an isosceles right triangle, therefore 15 must be equal to x, let's check that out using pythagorean theorem:

`\begin{gathered} (15\sqrt[]{2})^2=15^2+x^2 \\ x=\sqrt[]{(15\sqrt[]{2})^2-15^2} \\ x=\sqrt[]{450-225} \\ x=\sqrt[]{225} \\ x=15 \end{gathered}`

Therefore, we can conclude that Tameka is correct. It is a 45-45-90 triangle.

Let's check the perimeter:

`P=15+15+15\sqrt[]{2}=30+15\sqrt[]{2}\\e45\sqrt[]{2}`

Thus, the only correct statements are:

B. Tameka is correct. It is a 45-45-90 triangle

D. The measure of the remaining leg is also 15