Question

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: Apply Pythagorean theorem

Let \(a = 16\), \(b=20\), and \(c\) be the hypotenuse. By \(c=\sqrt{a^{2}+b^{2}}\), we have \(c=\sqrt{16^{2}+20^{2}}\).

Step2: Calculate \(a^{2}+b^{2}\)

\(16^{2}=256\), \(20^{2} = 400\). Then \(a^{2}+b^{2}=256 + 400=656\).

Step3: Calculate \(c\)

\(c=\sqrt{656}\approx25.6\)

Step4: Compare with the estimate

The estimate is \(25\). The difference is \(25.6-25 = 0.6\)

Answer:

It is under by approximately \(0.6\) units.