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skad [1K]
2 years ago
14

ABC with altitude \overline{BD}

Mathematics
1 answer:
just olya [345]2 years ago
8 0

The length of \overline{AC} is given by the relationship between the similar triangles

ΔABD and ΔBDC.

  • \overline{AC} = <u>80</u>

Reasons:

The given parameters are;

The altitude of triangle ΔABD = \overline {BD}

The hypotenuse of formed right triangle = \overline {AC}

The length of AD = 8

Length of BD = 24

Whereby  ΔABD is a right triangle

We have;

ΔABD is similar to ΔBDC

Therefore, by similar triangle proportional sides relationship, we have;

\displaystyle \frac{\overline{AD}}{\overline{BD}}  = \mathbf{ \frac{\overline{BD}}{\overline{DC}}}

Which gives;

\overline{BD}^2 = \mathbf{\overline{DC} \times \overline{AD}}

Therefore;

\displaystyle \overline{DC} = \mathbf{\frac{\overline{BD}^2}{\overline {AD}}}

\displaystyle \overline{DC} = \frac{24^2}{8} = \mathbf{72}

\overline{AC} = \overline{DC} + \overline{AD}

Which gives;

\overline{AC} = 72 + 8 =\mathbf{ 80}

Learn more about similar triangles here:

brainly.com/question/4618367

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