How do you determine if the lengths #3, 2sqrt10, sqrt41# form a right triangle?

Question

Hazel Anglin · Accepted Answer

The Pythagorean Theorem finds any side of a right triangle given the two other sides. We can use this theorem to see if these lengths of sides form a right triangle. The Pythagorean Theorem Formula is #a^2 + b^2 = c^2#, where #a# and #b# are the lengths of the sides of the triangle and #c# is the hypotenuse, or the longest side. Therefore, we can set up an equation with the longest side being #c#:
#3^2 + (2sqrt10)^2 = (sqrt41)^2# Simplify:
#9 + 4*10 = 41# #9 + 40 = 41# #49 = 41# No, #49# does NOT equal #41#. Therefore, these lengths do not form a right triangle.

Eva Adamson · Answer

undefined To determine if the lengths 3, 2√10, and √41 form a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, if the lengths 3, 2√10, and √41 form a right triangle, then the following equation should hold true:

(3)^2 + (2√10)^2 = (√41)^2

Simplifying the equation:

9 + 4(10) = 41

9 + 40 = 41

49 = 41

Since the equation is not true, the lengths 3, 2√10, and √41 do not form a right triangle.