2) which set of measure could be the side lengths of a right triangle?
A. 0.9 cm, 1.2 cm, 1.5 cm
B. 4 in, 4 in, 4 in
C. 7 m, 8m, 9m******
D. 2ft, 3ft, 4ft
nope. Think of your ubiquitous 3-4-5 right triangle
(A) is that same triangle, scaled by .3
It's obvious that (C) is wrong, since 7^2+8^2 = 49+64 = 113, not 9^2=81
On a question like this, even if you're guessing, at least check to make sure your answer fits!
To determine if a set of measures could be the side lengths of a right triangle, you need to apply the Pythagorean theorem. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's apply this theorem to each set of measures:
A. 0.9 cm, 1.2 cm, 1.5 cm
By squaring each side length, we get:
(0.9 cm)^2 = 0.81 cm^2
(1.2 cm)^2 = 1.44 cm^2
(1.5 cm)^2 = 2.25 cm^2
Now, let's check if the sum of the squares of the two shorter sides equals the square of the longest side:
0.81 cm^2 + 1.44 cm^2 = 2.25 cm^2
The sum of the squares of the two shorter sides is not equal to the square of the longest side. Therefore, this set of measures cannot be the side lengths of a right triangle.
B. 4 in, 4 in, 4 in
By squaring each side length, we get:
(4 in)^2 = 16 in^2
(4 in)^2 = 16 in^2
(4 in)^2 = 16 in^2
Now, let's check if the sum of the squares of the two shorter sides equals the square of the longest side:
16 in^2 + 16 in^2 = 32 in^2
The sum of the squares of the two shorter sides is not equal to the square of the longest side. Therefore, this set of measures cannot be the side lengths of a right triangle.
C. 7 m, 8 m, 9 m
By squaring each side length, we get:
(7 m)^2 = 49 m^2
(8 m)^2 = 64 m^2
(9 m)^2 = 81 m^2
Now, let's check if the sum of the squares of the two shorter sides equals the square of the longest side:
49 m^2 + 64 m^2 = 113 m^2
The sum of the squares of the two shorter sides is equal to the square of the longest side. Therefore, this set of measures could be the side lengths of a right triangle.
D. 2 ft, 3 ft, 4 ft
By squaring each side length, we get:
(2 ft)^2 = 4 ft^2
(3 ft)^2 = 9 ft^2
(4 ft)^2 = 16 ft^2
Now, let's check if the sum of the squares of the two shorter sides equals the square of the longest side:
4 ft^2 + 9 ft^2 = 13 ft^2
The sum of the squares of the two shorter sides is not equal to the square of the longest side. Therefore, this set of measures cannot be the side lengths of a right triangle.
Hence, the correct answer is C. 7 m, 8 m, 9 m.