The length of the hypotenuse of a right triangle is �ã2 times the length of one of the legs of the triangle.
answer choice:
a.Always true b. sometimes true c. never true
Only true in an isosceles right-angled triangle, i.e the other angles are 45° each
To determine the correct answer, we need to understand the relationship between the length of the hypotenuse and the length of the legs in a right triangle.
In a right triangle, the hypotenuse is the side opposite the right angle and is always the longest side. The lengths of the legs can vary depending on the triangle.
Since we are given that the length of the hypotenuse is √2 times the length of one of the legs, we can consider different scenarios:
Scenario 1: The length of the hypotenuse is √2 times the length of both legs.
If this is the case, then the answer would be "always true." In this scenario, both legs would be equal in length, and the length of the hypotenuse would be √2 times the length of each leg.
Scenario 2: The length of the hypotenuse is √2 times the length of only one leg.
If this is the case, then the answer would be "sometimes true." In this scenario, one leg would be different in length from the other, and the length of the hypotenuse would be √2 times the length of that leg.
Scenario 3: The length of the hypotenuse is not √2 times the length of any leg.
If this is the case, then the answer would be "never true." In this scenario, the length of the hypotenuse would not be √2 times the length of any leg.
Based on these scenarios, the correct answer would be b. sometimes true, as it is possible for the length of the hypotenuse to be √2 times the length of one of the legs in a right triangle.