Pythagorean Theorem: a^2 + b^2 = c^2
1 answer:
9514 1404 393
Answer:
No. Since 7^2 + 9^2 ≠ 11^2, the triangle cannot be a right triangle.
Step-by-step 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 <em>not a multiple of 3, 4, 5</em>, 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
You might be interested in