Given right triangle ABCABC with altitude \overline{BD}
2 answers:
Answer:
![x = 2\sqrt{11}](https://tex.z-dn.net/?f=%20x%20%3D%202%5Csqrt%7B11%7D%20)
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}](https://tex.z-dn.net/?f=%20BD%20%3D%20%5Csqrt%7BAD%2ADC%7D%20)
Plug in the values
![BD = \sqrt{4*7}](https://tex.z-dn.net/?f=%20BD%20%3D%20%5Csqrt%7B4%2A7%7D%20)
![BD = 2\sqrt{7}](https://tex.z-dn.net/?f=%20BD%20%3D%202%5Csqrt%7B7%7D%20)
Use pythagorean theorem to find x:
x² = AD² + BD²
Plug in the values
![x^2 = 4^2 + (2\sqrt{7})^2](https://tex.z-dn.net/?f=%20x%5E2%20%3D%204%5E2%20%2B%20%282%5Csqrt%7B7%7D%29%5E2%20)
![x^2 = 4^2 + (2\sqrt{7})^2](https://tex.z-dn.net/?f=%20x%5E2%20%3D%204%5E2%20%2B%20%282%5Csqrt%7B7%7D%29%5E2%20)
![x^2 = 16 + (4*7)](https://tex.z-dn.net/?f=%20x%5E2%20%3D%2016%20%2B%20%284%2A7%29%20)
![x^2 = 16 + 28](https://tex.z-dn.net/?f=%20x%5E2%20%3D%2016%20%2B%2028%20)
![x^2 = 44](https://tex.z-dn.net/?f=%20x%5E2%20%3D%2044%20)
Take the square root of both sides
![\sqrt{x^2} = \sqrt{44}](https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%5E2%7D%20%3D%20%5Csqrt%7B44%7D%20)
![x = \sqrt{44}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Csqrt%7B44%7D%20)
![x = \sqrt{4 * 11}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Csqrt%7B4%20%2A%2011%7D%20)
![x = 2\sqrt{11}](https://tex.z-dn.net/?f=%20x%20%3D%202%5Csqrt%7B11%7D%20)
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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