In the diagram below, the length of the legs AC and BC of right
triangle ABC are 6 cm and 8 cm, respectively. Altitude CD is drawn
to the hypotenuse of △ABC.
What is the length of AD to the nearest tenth of a centimeter?
To find the length of AD, we can use the concept of similar triangles. In right triangle ABC, we have an altitude drawn to the hypotenuse CD. This means that triangle ACD is similar to triangle BCD.
Since triangles ACD and BCD are similar, we can set up a proportion to find the length of AD.
Let x be the length of AD.
By the property of similar triangles, we can set up the following proportion:
AC/AD = BC/CD
Plugging in the given values:
6/x = 8/(x + 8)
To solve this proportion, we can use cross multiplication:
8 * x = 6 * (x + 8)
8x = 6x + 48
2x = 48
x = 24
Therefore, the length of AD is 24 cm.
by similar triangles, since angle B is common to both ABC and CBD, and AB = 10,
6/10 = AD/8
AD = 4.8