What is the length of the altitude drawn to the hypotenuse? The figure is not drawn to scale. Any help is appreciated, thank you!

Question

asked Nov 6, 2018 234k views

1 Answer

Rounds · Answer 1 · 2018-11-11T13:17:57+0000

Answer:

Explanation:

Consider the figure, in Triangle ABC and triangle BDC, we have

∠ABC=∠BDC (90°)

∠C=∠C (reflexive)

Thus, by AA similarity rule, ΔABC is similar to ΔBDC.

Therefore, using the similarity condition,

(AD)/(BD)=(BD)/(DC)

$(DB)^2=14{*}5$

(DB)^2=70

DB=√(70)

Thus, the length of the altitude=
√(70)