Triangles and Altitudes

Geometry Level pending

A B C ABC is a triangle with A = 13 c m A = 13cm , B C = 15 c m BC = 15cm and C A = 14 c m CA = 14cm , A D AD and B E BE are the altitudes from A A and B B to B C BC and A C AC respectively. H H is the point of intersection of A D AD and B E BE then the ratio 5 H D H B \frac{5HD}{HB} = ?


The answer is 3.

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1 solution

Saya Suka
May 11, 2021

Answer
= 5[(4/5) × 14 – (5/4) × 5] / [12 – (3/4) × 5]
= 5[56/5 – 25/4] / [12 – 15/4]
= (56 – 125/4) / (12 – 15/4)
= (224 – 125) / (48 – 15)
= 99 / 33
= 3


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