Answer:
The correct answer is (D).
Step-By-Step-Explanation:
A right triangle is a triangle in which one angle is a right angle, or 90 degrees. The sum of the other two angles in a right triangle is always 90 degrees.
To determine if a set of side measurements could be used to form a right triangle, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse.
In (A), \sqrt{19} and \sqrt{35} are the legs of the triangle, and 54 is the hypotenuse. Plugging these values into the Pythagorean theorem, we get:
(\sqrt{19})^2 + (\sqrt{35})^2 = 54^2
19 + 35 = 284
284 \neq 2916
Since the left-hand side of the equation does not equal the right-hand side, we know that (A) is not a right triangle.
In (B), \sqrt{15} and 6 are the legs of the triangle, and \sqrt{51} is the hypotenuse. Plugging these values into the Pythagorean theorem, we get:
(\sqrt{15})^2 + 6^2 = (\sqrt{51})^2
225 + 36 = 51
261 \neq 261
Since the left-hand side of the equation does not equal the right-hand side, we know that (B) is not a right triangle.
In (C), 5, 8, and 30 are the side measurements of the triangle. Plugging these values into the Pythagorean theorem, we get:
5^2 + 8^2 = 30^2
25 + 64 = 900
89 = 900
Since the left-hand side of the equation does not equal the right-hand side, we know that (C) is not a right triangle.
In (D), 5, 6, and 7 are the side measurements of the triangle. Plugging these values into the Pythagorean theorem, we get:
5^2 + 6^2 = 7^2
25 + 36 = 49
61 = 49
Since the left-hand side of the equation equals the right-hand side, we know that (D) is a right triangle
