Question

a right triangle has side lengths 4 units, 5 units, and x units. it is unknown if the missing length is the longest or shortest side.
rounded to the nearest tenth, what is the difference between the possible values of x?
3.0 units
3.4 units
6.4 units
8.0 units

Explanation:

Step1: Apply Pythagorean theorem when \(x\) is the hypotenuse

If \(x\) is the hypotenuse, by Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (where \(c\) is the hypotenuse), we have \(4^{2}+5^{2}=x^{2}\).
So \(x=\sqrt{16 + 25}=\sqrt{41}\approx6.4\).

Step2: Apply Pythagorean theorem when \(x\) is a leg

If \(x\) is a leg (assume \(5\) is the hypotenuse), then \(x^{2}+4^{2}=5^{2}\).
So \(x=\sqrt{25 - 16}=\sqrt{9}=3\).

Step3: Calculate the difference

The difference between the two possible values of \(x\) is \(6.4−3 = 3.4\).

Answer:

3.4 units