Question

applying the converse of the pythagorean theorem
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?
16
20
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: Assume right triangle, use Pythagoras

$$c = \sqrt{16^2 + 20^2}$$

Step2: Calculate squared terms

$$16^2 = 256, 20^2 = 400$$

Step3: Sum and compute square root

$$c = \sqrt{256 + 400} = \sqrt{656} \approx 25.61$$

Step4: Compare estimate to actual

$$25 - 25.61 \approx -0.61$$

Answer:

It is over by approximately 0.6 units.