Question

consider triangle ghj.
what is the length of line segment hj?
5 units
5√3 units
10 units
10√3 units

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle \(GHJ\) with right - angle at \(H\), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = JG=10\) (hypotenuse) and \(a = GH = 5\), and \(b=HJ\).
So, \(HJ^{2}+GH^{2}=JG^{2}\).

Step2: Substitute values

Substitute \(GH = 5\) and \(JG = 10\) into the formula:
\(HJ^{2}+5^{2}=10^{2}\).
\(HJ^{2}+25 = 100\).
\(HJ^{2}=100 - 25\).
\(HJ^{2}=75\).

Step3: Solve for \(HJ\)

\(HJ=\sqrt{75}=\sqrt{25\times3}=5\sqrt{3}\).

Answer:

\(5\sqrt{3}\text{ units}\)