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stepan [7]
3 years ago
14

Given right triangle ABCABC with altitude \overline{BD}

Mathematics
2 answers:
Alex3 years ago
6 0

Answer:

x = 2\sqrt{11}

Step-by-step explanation:

AD = 4

AC = 11

DC = 11 - 4 = 7

First, find BD using the right triangle altitude theorem:

BD = \sqrt{AD*DC}

Plug in the values

BD = \sqrt{4*7}

BD = 2\sqrt{7}

Use pythagorean theorem to find x:

x² = AD² + BD²

Plug in the values

x^2 = 4^2 + (2\sqrt{7})^2

x^2 = 4^2 + (2\sqrt{7})^2

x^2 = 16 + (4*7)

x^2 = 16 + 28

x^2 = 44

Take the square root of both sides

\sqrt{x^2} = \sqrt{44}

x = \sqrt{44}

x = \sqrt{4 * 11}

x = 2\sqrt{11}

Ahat [919]3 years ago
6 0

Answer:

6

Step-by-step explanation:

\frac{\color{darkorange}{x}}{\color{darkgreen}{4}}=

4

x

​

=

\,\,\frac{\color{darkorange}{9}}{\color{darkgreen}{x}}

x

9

​

Use the longer leg over the shorter leg in the smaller triangle and the middle triangle

x^2=

x

2

=

\,\,36

36

Multiply both sides by 44 and xx

\sqrt{x^2}=

x

2

​

=

\,\,\sqrt{36}

36

​

Square root both sides

x=

x=

\,\,6

6

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