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lilbrown6369
06.06.2021 •
Mathematics
THIRD TIME ASKING FOR HELP PLEASE HELP ME Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB=3 and AD=1, what is the length of AC?
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Ответ:
Explanation:
For now, focus on triangle ABD. This is a right triangle due to BD being an altitude.
Use the pythagorean theorem to find that...
(AD)^2 + (BD)^2 = (AB)^2
(1)^2 + (BD)^2 = (3)^2
1 + (BD)^2 = 9
(BD)^2 = 9-1
(BD)^2 = 8
Normally we would isolate BD itself, but I'll stop short and use that last line instead.
The triangles ABD and BCD are similar triangles (we can prove this using the AA similarity theorem).
Since we have similar triangles, we can form the proportion shown below
AD/BD = BD/CD
This cross multiplies to
AD*CD = (BD)^2
We know that AD = 1 and (BD)^2 = 8, so,
AD*CD = (BD)^2
1*CD = 8
CD = 8
This then means,
x = CD+DA
x = 8+1
x = 9
AC is 9 units long.
Ответ:
x-3y=30 | ×2
21x + 6y = 9
2x - 6y = 60 +
23x / = 69
x = 69:23
x = 3
7x + 2y = 3
21 + 2y = 3
2y = -18
y = -9