Question

rosemary is cutting 3 wooden sticks to build part of a kite frame. the part she is building must be a right triangle. which choice below could be the lengths, in inches, of the sticks rosemary cut? 6,8,10 5,6,7 2,3,5 2,5,10

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the sum of the squares of the two shorter sides (legs) should equal the square of the longest side (hypotenuse), i.e., \(a^2 + b^2 = c^2\) where \(c\) is the hypotenuse.

Step2: Check option 6,8,10

Calculate \(6^2 + 8^2\) and \(10^2\).
\(6^2 = 36\), \(8^2 = 64\), so \(6^2 + 8^2 = 36 + 64 = 100\).
\(10^2 = 100\). Since \(6^2 + 8^2 = 10^2\), this satisfies the Pythagorean theorem.

Step3: Check option 5,6,7

Calculate \(5^2 + 6^2\) and \(7^2\).
\(5^2 = 25\), \(6^2 = 36\), so \(5^2 + 6^2 = 25 + 36 = 61\).
\(7^2 = 49\). Since \(61
eq49\), this does not satisfy the theorem.

Step4: Check option 2,3,5

First, check triangle inequality (sum of two sides > third side). \(2 + 3 = 5\), which is not greater than 5, so it's not a valid triangle.

Step5: Check option 2,5,10

Check triangle inequality: \(2 + 5 = 7 < 10\), so it's not a valid triangle.

Answer:

6, 8, 10