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Radda [10]
2 years ago
13

Given right triangle ABCABC with altitude \overline{BD} BD drawn to hypotenuse ACAC. If BC=10BC=10 and DC=5,DC=5, what is the le

ngth of \overline{AC}? AC ?
Mathematics
2 answers:
Helen [10]2 years ago
5 0

Answer: \overline{AC}= 12.5

Step-by-step explanation: The triangle ABC and its altitude \overline{BD} is represented in the figure below.

<u>Altitude</u> is a segment of line that link a vertex and the opposite side, forming a right angle.

So, because of \overline{BD}, now we have two similar triangles, which means that ratios of corresponding sides are equal:

\frac{\overline{BD}}{\overline{BC}} =\frac{\overline{AD}}{\overline{BD}}

\overline{BD}^{2}=\overline{BC}.\overline{AD} (1)

This is always true for a right triangle and a altitude drawn to the hypotenuse.

Triangle BDC is also right triangle. So, we can use Pythagorean theorem to determine the missing side.

\overline{BC}^{2}=\overline{CD}^{2}+\overline{BD}^{2}

\overline{BD}^{2}=\overline{BC}^{2}-\overline{CD}^{2} (2)

Substituting (2) into (1):

\overline{BC}^{2}-\overline{CD}^{2}=\overline{BC}.\overline{AD}

We want to find f, so:

\overline{AD}=\frac{\overline{BC}^{2}-\overline{CD}^{2}}{\overline{BC}}

f=\frac{10^{2}-5^{2}}{10}

f = 7.5

The length of \overline{AC} is

\overline{AC}=f+5

\overline{AC}=7.5+5

\overline{AC}=12.5

The length of the hypotenuse of triangle ABC is 12.5 units.

e-lub [12.9K]2 years ago
3 0

Answer:

x = 20

Step-by-step explanation:

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