in a right triangle ABC, if ab is 14 and bc is 12 wut is bd?
there is a pic of a large trangle abc and in it is a line drawn down angle c making it line cd. angle acd then becomes a right trangle as well.
i tried working = proportions and pyth thm but i don't seem to be getting the right answer. i also no theses r simialiar triangles. the answer is 72/7 but i don't no how.
I will assume in your triangle ABC, angle C is the right angle.
Make three columns, one for each of the angles, listing the sides given under each angle for the large triangle and the similar smaller one
A....B....C
12...√52..14 ( I found √52 by Pythagoras)
BD....CD..12
Now set up your ratios:
BD/12 = 12/14 which will give you BD = 72/7
To find the length of BD in the right triangle ABC, you can use the concept of similar triangles. Since triangle ABC and triangle ACD are similar, their corresponding sides are proportional.
Let's set up the ratios:
For the larger triangle ABC:
AB/BC = 14/12
AB = 14/12 * 12 = 14
For the smaller triangle ACD:
AC/CD = 14/12
Now, you are trying to find the length of BD. Let's call BD as x.
In the smaller triangle ACD, using the Pythagorean theorem, we have:
AC^2 = CD^2 + AD^2
14^2 = 12^2 + AD^2
196 = 144 + AD^2
AD^2 = 196 - 144
AD^2 = 52
Now, in the smaller triangle ABD:
AB/BD = AD/CD
14/x = √52/12
To solve for x (BD), cross-multiply:
√52 * BD = 14 * 12
BD√52 = 168
To isolate BD, divide both sides of the equation by √52:
BD = 168 / √52
To simplify the square root, we can rationalize the denominator:
BD = 168(√52) / (√52 * √52)
BD = 168√52 / 52
BD = (168/52)√52
BD = 72/7 * √52
Therefore, the length of BD is 72/7.