A right isosceles triangle is cut out from a piece of sheet metal. The two equal sides are 1.0 m long each. How far is the center of gravity from the right angle (90. °) vertex of the triangle?
A) 0.24 m
B) 0.55 m
C) 0.47 m
D) 0.71 m
E) 0.35 m

Question

Quizplus · Accepted Answer

The center of gravity (centroid) of a triangle is located at a point where the three medians intersect. For any triangle, this point is located at a distance of 1/3 the length of the median from each vertex. In a right isosceles triangle, the median from the right angle vertex to the hypotenuse bisects the right angle, creating two 45-45-90 triangles. The length of this median can be found using the Pythagorean theorem, where the median (m) is the hypotenuse of these smaller triangles, and the legs are each 1/2 the length of the hypotenuse of the original triangle. Thus, $m = \sqrt{(0.5)^2 + (0.5)^2} = \sqrt{0.25 + 0.25} = \sqrt{0.5} = 0.7071$ meters. The centroid is 1/3 of the way along this median from the right angle, so the distance is $0.7071 \times \frac{1}{3} \approx 0.2357$ meters, which rounds to 0.24 meters, making the correct choice based on the options provided actually A, not C. My initial statement of choice C was incorrect based on the calculation provided. The correct answer, based on the calculation, should be A, 0.24 meters.

A Right Isosceles Triangle Is Cut Out from a Piece