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Answer :
Final answer:
To determine if the measurements could be the side lengths of a right triangle, we can apply the Pythagorean theorem by calculating the squares of the given side lengths and comparing them to the square of the longest side. Option B (66 in, 88 in, 110 in) satisfies the theorem and can represent the side lengths of a right triangle.
Explanation:
To determine which of the given measurements can represent the side lengths of a right triangle, we can apply the Pythagorean theorem. According to the theorem, in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (hypotenuse). Let's calculate the squares of the side lengths and check which measurements satisfy the theorem:
A. (55in)2 + (88in)2 = 3025in2 + 7744in2 = 10769in2
B. (66in)2 + (88in)2 = 4356in2 + 7744in2 = 120100in2
C. (66in)2 + (99in)2 = 4356in2 + 9801in2 = 14157in2
D. (66in)2 + (88in)2 = 4356in2 + 7744in2 = 120100in2
Based on the calculations, we can see that option B (66 in, 88 in, 110 in) satisfies the Pythagorean theorem and can represent the side lengths of a right triangle.
Learn more about Pythagorean theorem here:
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Option B forms a right triangle.
To determine which set of measurements could form the side lengths of a right triangle, you can apply the Pythagorean theorem.
The correct measurements for a right triangle should satisfy the Pythagorean theorem, which states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
A. 55 in, 88 in, 110 in: 55² + 88² = 3025 + 7744 = 10769; while 110² = 12100.
Not a right triangle.
B. 66 in, 88 in, 110 in: 66² + 88² = 4356 + 7744 = 12100; 110² = 12100.
This set of measurements forms a right triangle.
C. 66 in, 99 in, 110 in: 66² + 99² = 4356 + 9801 = 14157; 110² = 12100.
Not a right triangle.
D. 66 in, 88 in, 132 in: 66² + 88² = 4356 + 7744 = 12100; 132² = 17424.
Not a right triangle.
Therefore, option B with sides 55 in, 88 in, 110 in forms a right angled triangle.
