Question

what is the length of \overline{df}?

a 24 in.
b 28 in.
c 10 in.
d 100 in.

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle \(DEF\) with \(DE = 8\) in and \(EF=6\) in, by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 6\), \(b = 8\) and \(c=\overline{DF}\).
So, \(DF^{2}=DE^{2}+EF^{2}\).

Step2: Substitute values

Substitute \(DE = 8\) and \(EF = 6\) into the formula:
\(DF^{2}=8^{2}+6^{2}\)
\(DF^{2}=64 + 36\)
\(DF^{2}=100\)

Step3: Solve for \(DF\)

Take the square root of both sides:
\(DF=\sqrt{100}\)
\(DF = 10\)

Answer:

C. 10 in.