Triangle similarity problem

Geometry Level 1

Find H J HJ .

6 27 9 11 \frac{9}{11} 91 4 \frac{91}{4}

Harsh Chaudhari by Harsh Chaudhari , 36, India

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2 solutions

Mahdi Raza
Apr 20, 2020

[ Δ F G I ] ∼ [ Δ F H J ] ⟹ F G G I = F H H J [\Delta FGI] \sim [\Delta FHJ] \implies \frac{FG}{GI} = \frac{FH}{HJ}

4 7 = 4 + 7 x ⟹ x = 91 4 \frac{4}{7} = \frac{4 + 7}{x} \implies x = \boxed{\frac{91}{4}}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

F G G I = F H H J \dfrac{FG}{GI}=\dfrac{FH}{HJ}

4 7 = 13 H J \dfrac{4}{7}=\dfrac{13}{HJ}

H J = 91 4 HJ = \dfrac{91}{4}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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