Question

What is the length of the altitude drawn to the hypotenuse? The figure is not drawn to scale.

Any help is appreciated, thank you!

Answer 1

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)`