To find the length of the hypotenuse in a right triangle, you can use the Pythagorean theorem, which states:
\[ c^2 = a^2 + b^2 \]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two legs. In this case, let \(a = 10 , \text{cm}\) and \(b = 14 , \text{cm}\).
Now, calculate \(c\):
\[ c^2 = 10^2 + 14^2 \] \[ c^2 = 100 + 196 \] \[ c^2 = 296 \]
Now, take the square root of both sides to find \(c\):
\[ c = \sqrt{296} \] \[ c \approx 17.2 , \text{cm} \]
Therefore, the length of the hypotenuse is approximately 17.2 cm when rounded to the nearest tenth.