Question

consider triangle ghj.
what is the length of line segment hj?
j----10----g
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h----g (with right angle at h, hg=5)
options: 5 units, 5√3 units, 10 units, 10√3 units

Explanation:

Step1: Identify triangle type

Triangle \( GHJ \) is right - angled at \( H \), with hypotenuse \( JG = 10 \) and leg \( GH = 5 \). Let \( HJ=x \).

Step2: Apply Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with hypotenuse \( c \) and legs \( a,b \), \( c^{2}=a^{2}+b^{2} \). Here, \( c = JG = 10 \), \( a=GH = 5 \), \( b = HJ=x \). So, \( 10^{2}=5^{2}+x^{2} \).

Step3: Solve for \( x \)

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Answer:

\( 5\sqrt{3} \) units (corresponding to the option " \( 5\sqrt{3} \) units")