To find the length of the altitude to the hypotenuse in the given right triangle (sides 5,12,13), follow these steps:
The area of a right triangle can be calculated in two ways:
Using the legs as base and height:
[ \text{Area} = \frac{1}{2} \times \text{leg}_1 \times \text{leg}_2 = \frac{1}{2} \times 5 \times 12 = 30 ]
Using the hypotenuse and its altitude ((h)):
[ \text{Area} = \frac{1}{2} \times \text{hypotenuse} \times h = \frac{1}{2} \times 13 \times h ]
[ \frac{1}{2} \times 13 \times h = 30 ]
[ 13h = 60 ]
[ h = \frac{60}{13} \approx 4.62 ]
Answer: The length of the altitude to the hypotenuse is (\boxed{\dfrac{60}{13}}) (or approximately 4.62).
(\boxed{4.62}) (rounded to two decimal places) or (\boxed{\dfrac{60}{13}}) (exact value).
Since the problem might expect a numerical approximation, the final answer is:
(\boxed{4.62})
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