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

Hello!

Well, the altitude of a right triangle = sqrt of the two lengths it divides the hypotenuse into so in your problem, the altitude = sqrt of 5(14).

the 2 triangles ACD and ABC are similar (same shape - corresponding angles are equal) the property of similar triangles is that corresponding sides are in the same ratio.

Hope this all Helps! :)

Answer 2

Answer:

Step-by-step 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,

$\frac{AD}{BD}=\frac{BD}{DC}$

$(DB)^2=14{\times}5$

$(DB)^2=70$

$DB=\sqrt{70}$

Thus, the length of the altitude= $\sqrt{70}$