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sweet [91]
3 years ago
5

In triangle $ABC,$ point $D$ is on $\overline{AC}$ such that $AD = 3CD = 12$. If $\angle ABC = \angle BDA = 90^\circ$, then what

is $BD$?

Mathematics
1 answer:
Neporo4naja [7]3 years ago
8 0

Answer:

BD=4\sqrt{3}\ units

Step-by-step explanation:

we know that

AD=12\ units

3CD=12 ----> CD=4\ units

see the attached figure to better understand the problem

Triangles ABD and BCD are similar by AA Similarity Theorem

Remember that

If two figures are similar, then the ratio of its corresponding sides is proportional

so

\frac{BD}{AD}=\frac{CD}{BD}

substitute the given values

\frac{BD}{12}=\frac{4}{BD}

BD^2=48

BD=\sqrt{48}\ units

simplify

BD=4\sqrt{3}\ units

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There are a total of 21 students in the choir and the drama club. There are 7 more students in the choir than the drama club. Wr
PolarNik [594]

Answer:

<em>The number of students in the drama club is 7 and the number in the choir is 14</em>

Step-by-step explanation:

X = Number of students in choir club

Y =  Number of students in drama club

<u>First equation:</u>

x + y = 21

<u></u>

<u>Since we know that there are 7 more students in the choir club than the drama club, that means:</u>

x + 7 = y

<u>A little trick that you can do to find y is this:</u>

21 students in the choir and drama club - 7

=> 14

Meaning that y is 14

<u>So lets go back into our second equation:</u>

x + 7 = 14

7 + 7 =14

x=7

<u>Plug both variables in:</u>

7 + 14 = 21

So that means that there are 7 students in the drama club and 14 students in the choir club.

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3 years ago
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solniwko [45]

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