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Taya2010 [7]
3 years ago
15

In the right triangle below, an altitude is drawn to the hypotenuse. Solve for x.

Mathematics
1 answer:
svet-max [94.6K]3 years ago
4 0

Answer:

x = 3√7

Step-by-step explanation:

From the right triangle given in the picture,

Altitude or height of the triangle (AD) = x

Base or hypotenuse of the given triangle (BC) = 16

Length of segment BD = 16 - 7 = 9

By using geometric mean theorem in the given triangle,

\frac{AD}{BD}=\frac{DC}{AD}

(AD)² = (BD)(CD)

x² = 9×7

x = √63

x = 3√7

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How would I solve <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20x-%5Cfrac%7B5%7D%7B3%7D%20%3D-%5Cfrac%7B1%7D%7B2%7D%
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Multiply both sides of the equation by 12. Move the variables to the left-hand side and change its sign. Move the constant to the left-hand side and change its sign. Collect like terms. Add the numbers. Divide both sides of the equation by 12.

1/2 x - 5= - 1/2 x + 19/4
6x -20= - 6x + 57
6x + 6x= 57 + 20
12x= 57 + 20
12x= 77
ANSWER
x = 77/12
Alternative Form .
x = 6 5/12, x= 6.416
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3 years ago
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