Question

If an altitude is drawn from the right angle of a right triangle to its hypotenuse, the two segments formed on the hypotenuse are 11.25 cm and 5 cm, then what is the length of the altitude?

Answer 1

Answer:

the length of the altitude is 7.5 cm

Step-by-step explanation:

In a Δ ABC, $\overline {BC}$ is the altitude

If an altitude is drawn to the hypotenuse of the right angle triangle as shown in the image attached below; Then:

$(AD)^2 = AD*AC \\ \\ x^2 = 5*11.25 \\ \\ x^2 = 81.25 \\ \\ x = \sqrt{81.25} \\ \\ x= 9.01$

NOW;

$(BC)^2 = DC*AC \\ \\ z^2 = 11.25 *16.25 \\ \\z^2 = 182.8125 \\ \\ z= \sqrt{182.8125} \\ \\ z= 13.52$

Finally; the altitude which is $\overline {BD}$ is calculated as:

$(BD)^2 = AD*DC \\ \\ y^2 = 5*11.25 \\ \\ y^2 = 56.25 \\ \\ y = \sqrt{56.25} \\ \\ y= 7.5$

Thus; the length of the altitude is 7.5 cm