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 right - triangle GHJ, if the hypotenuse is GJ = 10 and one leg is GH = 5. Let HJ be the other leg. According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. So \(HJ=\sqrt{GJ^{2}-GH^{2}}\).

Step2: Substitute the values

Substitute \(GJ = 10\) and \(GH = 5\) into the formula: \(HJ=\sqrt{10^{2}-5^{2}}=\sqrt{100 - 25}=\sqrt{75}=5\sqrt{3}\).

Answer:

B. \(5\sqrt{3}\) units