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The lengths of the sides of a right triangle are 2√3 cm and 3√7cm. Find the length of the hypotenuse of the triangle.​

User Jslap
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Final answer:

To find the length of the hypotenuse of a right triangle with sides of 2√3 cm and 3√7 cm, we use the Pythagorean theorem and calculate √(75), which gives a hypotenuse of 5√3 cm.

Step-by-step explanation:

The student wishes to find the length of the hypotenuse of a right triangle with sides of lengths 2√3 cm and 3√7 cm. According to the Pythagorean theorem, which is given by the formula a² + b² = c², where a and b are the legs of the right triangle and c is the hypotenuse, we can calculate the length of the hypotenuse as follows:

Firstly, square the lengths of both sides:

  • (2√3)² = 4∙7 = 12
  • (3√7)² = 9∗49 = 63

Next, sum these values:

12 + 63 = 75

Finally, take the square root of this sum to find the length of the hypotenuse:

hypotenuse = √(75) = 5√3 cm

The length of the hypotenuse is therefore 5√3 cm.

User Daniel Kilinskas
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