Use the converse of the Pythagorean theorem to determine which of the following are side lengths of a right triangle.
A.
2.1, 2.8, and 3.5 units
B.
2.3, 2.8, and 3.6 units
C.
2.2, 2.9, and 3.6 units
D.
2.2, 2.7, and 3.5 units
C?
recall your 3-4-5 right triangle.
Multiply each side by 0.7 and you choice (A).
Or, you can just square all these numbers and see which two add up to the third in any given choice.
To determine which set of side lengths can form a right triangle, we can use the converse of the Pythagorean theorem. The theorem states that if the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
Let's calculate the square of the longest side for each set of side lengths:
A. Longest side = 3.5 units
Square of longest side = 3.5^2 = 12.25 units^2
B. Longest side = 3.6 units
Square of longest side = 3.6^2 = 12.96 units^2
C. Longest side = 3.6 units
Square of longest side = 3.6^2 = 12.96 units^2
D. Longest side = 3.5 units
Square of longest side = 3.5^2 = 12.25 units^2
Now, let's check if the square of the longest side is equal to the sum of the squares of the other two sides for each set:
A. Sum of squares of other two sides = 2.1^2 + 2.8^2 = 4.41 + 7.84 = 12.25 units^2
The square of the longest side and the sum of the squares of the other two sides are equal, so this set can form a right triangle.
B. Sum of squares of other two sides = 2.3^2 + 2.8^2 = 5.29 + 7.84 = 13.13 units^2
The square of the longest side and the sum of the squares of the other two sides are not equal, so this set cannot form a right triangle.
C. Sum of squares of other two sides = 2.2^2 + 2.9^2 = 4.84 + 8.41 = 13.25 units^2
The square of the longest side and the sum of the squares of the other two sides are not equal, so this set cannot form a right triangle.
D. Sum of squares of other two sides = 2.2^2 + 2.7^2 = 4.84 + 7.29 = 12.13 units^2
The square of the longest side and the sum of the squares of the other two sides are not equal, so this set cannot form a right triangle.
Therefore, the only set of side lengths that can form a right triangle is A. (2.1, 2.8, and 3.5 units).