Question

"Is this a right triangle? Triangle has side lengths 10 feet, √205 feet, and √105 feet. Explain."

Answer 1

Answer: Yes, it is a right triangle

Step-by-step explanation

Use a calculator to find these approximations

`√(205) \approx 14.31782\\\\√(105) \approx 10.24695`

The largest value is 14.31782 which corresponds to
`√(205)`. This is the hypotenuse, which is the value of c. The 'a' and b values are 10 and
`√(105)` in either order.

If we had a right triangle, then the pythagorean theorem equation
`a^2+b^2 = c^2` would be a true equation for those a,b,c values mentioned.

Let's plug in those values to see what happens when we simplify both sides as much as possible.

`a^2+b^2 = c^2\\\\10^2+(√(105))^2 = (√(205))^2\\\\100+105 = 205\\\\205 = 205\\\\`

The last equation is true, so the first equation is true when
`(a,b,c) = (10, √(105), √(205))` which confirms we have a right triangle.

Side note: This right triangle is scalene because all 3 sides are different lengths.