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.