If a right triangle has legs of lengths 3 cm and 4 cm, what is the length of the hypotenuse?

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Multiple Choice

If a right triangle has legs of lengths 3 cm and 4 cm, what is the length of the hypotenuse?

Explanation:
To find the length of the hypotenuse in a right triangle where the lengths of the legs are known, one can apply the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula can be expressed as: \[ c^2 = a^2 + b^2 \] In this case, the lengths of the legs are 3 cm and 4 cm. By substituting these values into the theorem, we calculate: \[ c^2 = 3^2 + 4^2 \] \[ c^2 = 9 + 16 \] \[ c^2 = 25 \] To find the length of the hypotenuse (c), take the square root of both sides: \[ c = \sqrt{25} \] \[ c = 5 \, \text{cm} \] Therefore, the length of the hypotenuse is 5 cm. This confirms the answer as being correct, as derived by using the appropriate mathematical principles that govern right triangles. The other choices do not satisfy the relationship

To find the length of the hypotenuse in a right triangle where the lengths of the legs are known, one can apply the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula can be expressed as:

[ c^2 = a^2 + b^2 ]

In this case, the lengths of the legs are 3 cm and 4 cm. By substituting these values into the theorem, we calculate:

[ c^2 = 3^2 + 4^2 ]

[ c^2 = 9 + 16 ]

[ c^2 = 25 ]

To find the length of the hypotenuse (c), take the square root of both sides:

[ c = \sqrt{25} ]

[ c = 5 , \text{cm} ]

Therefore, the length of the hypotenuse is 5 cm. This confirms the answer as being correct, as derived by using the appropriate mathematical principles that govern right triangles. The other choices do not satisfy the relationship

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