Question

Pythagorean Theorem: a^2 + b^2 = c^2

Question 6 options:


No. Since 7^2+9^2≠11^2, the triangle cannot be a right triangle.



Yes. Since 7^2+9^2=11^2, the triangle must be a right triangle.



Yes. Since7^2+9^2≠11^2, the triangle must be a right triangle.



No. Since 7^2+9^2=11^2, the triangle cannot be a right triangle.

Answer 1

9514 1404 393

Answer:

No. Since 7^2 + 9^2 ≠ 11^2, the triangle cannot be a right triangle.

Explanation:

You may recall that side lengths of 3, 4, 5 make a right triangle. That particular triple has several interesting characteristics. One is that it is the only (reduced) triple that is an arithmetic sequence (has a constant difference between the side lengths). Any right triangle that has sides that differ by a constant amount must be a multiple of 3, 4, 5.

Here, we have sides of length 7, 9, 11—values that differ by 2. They form an arithmetic sequence that is not a multiple of 3, 4, 5, so we know right away they cannot be sides of a right triangle.

__

If we want to use the Pythagorean relation to check, we can see if the equation is true:

7² + 9² = 11²

49 + 81 = 121

130 = 121 . . . . . . Not True