Question

consider triangle ghj. image of right triangle with jg=10, gh=5, right angle at h what is the length of line segment hj? ○ 5 units ○ 5√3 units ○ 10 units ○ 10√3 units

Explanation:

Step1: Identify triangle type

Triangle \( GHJ \) is right - angled at \( H \), so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with hypotenuse \( c \) and legs \( a \) and \( b \), \( c^{2}=a^{2}+b^{2} \). Here, \( JG = 10 \) (hypotenuse), \( GH = 5 \) (one leg), and \( HJ \) is the other leg. Let \( HJ=x \), \( GH = 5 \), \( JG=10 \).

Step2: Apply Pythagorean theorem

From \( c^{2}=a^{2}+b^{2} \), we can re - arrange it to find the length of a leg: \( a=\sqrt{c^{2}-b^{2}} \). Substituting \( c = 10 \) and \( b = 5 \) into the formula, we get \( x=\sqrt{10^{2}-5^{2}}=\sqrt{100 - 25}=\sqrt{75}=\sqrt{25\times3}=5\sqrt{3} \).

Answer:

\( 5\sqrt{3} \) units