If a triangle has sides measuring 60, 75, and 45, is it a right triangle?(1 point)
Responses
No, because 5,625 does not equal 3,600.
No, because 5,625 does not equal 3,600.
No, because 9,225 does not equal 2,025.
No, because 9,225 does not equal 2,025.
Yes, because 5,625 equals 5,625.
Yes, because 5,625 equals 5,625.
Yes, because 3,600 equals 3,600.
Yes, because 3,600 equals 3,600.
7 answers
No, because 5,625 does not equal 3,600.
If triangle DEF has sides measuring 50, 40, and 32, is the triangle a right triangle? If it is a right triangle, answer with the number 90. If it is not a right triangle, answer with the number 0.(1 point)
To determine if a triangle is a right triangle, we can use the Pythagorean theorem. In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's check if the lengths of the sides of triangle DEF follow this theorem:
50^2 = 2500
40^2 = 1600
32^2 = 1024
Since 2500 is not equal to the sum of 1600 and 1024, triangle DEF is not a right triangle.
Therefore, the answer is 0.
Let's check if the lengths of the sides of triangle DEF follow this theorem:
50^2 = 2500
40^2 = 1600
32^2 = 1024
Since 2500 is not equal to the sum of 1600 and 1024, triangle DEF is not a right triangle.
Therefore, the answer is 0.
If a triangle has sides of length 12 and 16, how long is the hypotenuse?(1 point)
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To find the length of the hypotenuse in a right triangle, we can use the Pythagorean theorem. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's use the Pythagorean theorem to find the length of the hypotenuse:
$$c^2 = a^2 + b^2$$
Given that side a = 12 and side b = 16, we can substitute these values into the equation:
$$c^2 = 12^2 + 16^2$$
$$c^2 = 144 + 256$$
$$c^2 = 400$$
To solve for c, we can take the square root of both sides of the equation:
$$c = \sqrt{400}$$
$$c = 20$$
Therefore, the length of the hypotenuse is 20 units.
Let's use the Pythagorean theorem to find the length of the hypotenuse:
$$c^2 = a^2 + b^2$$
Given that side a = 12 and side b = 16, we can substitute these values into the equation:
$$c^2 = 12^2 + 16^2$$
$$c^2 = 144 + 256$$
$$c^2 = 400$$
To solve for c, we can take the square root of both sides of the equation:
$$c = \sqrt{400}$$
$$c = 20$$
Therefore, the length of the hypotenuse is 20 units.
If a right triangle has a leg with length 12 and the hypotenuse is 16, how long is the other leg? Round to the nearest tenth, if necessary.(1 point)
To find the length of the other leg of a right triangle, we can again use the Pythagorean theorem. In a right triangle, the square of one leg is equal to the square of the hypotenuse minus the square of the other leg.
Let's use the Pythagorean theorem to find the length of the other leg:
$$a^2 = c^2 - b^2$$
Given that one leg (b) has a length of 12 and the hypotenuse (c) is 16, we can substitute these values into the equation:
$$a^2 = 16^2 - 12^2$$
$$a^2 = 256 - 144$$
$$a^2 = 112$$
To solve for a, we can take the square root of both sides of the equation:
$$a = \sqrt{112} \approx 10.6$$
Therefore, the length of the other leg is approximately 10.6 units rounded to the nearest tenth.
Let's use the Pythagorean theorem to find the length of the other leg:
$$a^2 = c^2 - b^2$$
Given that one leg (b) has a length of 12 and the hypotenuse (c) is 16, we can substitute these values into the equation:
$$a^2 = 16^2 - 12^2$$
$$a^2 = 256 - 144$$
$$a^2 = 112$$
To solve for a, we can take the square root of both sides of the equation:
$$a = \sqrt{112} \approx 10.6$$
Therefore, the length of the other leg is approximately 10.6 units rounded to the nearest tenth.
1 answer