Question

applying the converse of the pythagorean theorem
16 20
janice examines the given triangle and estimates that the longest side has a length of 25 units—if it is a right triangle. how does her estimate compare to the actual length?
it is exactly correct.
it is under by approximately 0.6 units.
it is over by approximately 0.6 units.
it is over by 13 units.

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here \(a = 16\) and \(b = 20\).

Step2: Calculate the length of the hypotenuse

\[c=\sqrt{16^{2}+20^{2}}=\sqrt{256 + 400}=\sqrt{656}\approx 25.6\]

Step3: Compare with the estimate

The estimate is 25 units. The difference is \(25.6−25 = 0.6\) units. Since \(25.6>25\), the estimate is under by approximately 0.6 units.

Answer:

It is under by approximately 0.6 units.