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Makovka662 [10]

3 years ago

6

The mathematical fact: a(b+c) = ab + ac ______________________________

1 answer:

Greeley [361]3 years ago

3 0

Answer:

Distributive law, in mathematics, the law relating the operations of multiplication and addition, stated symbolically, a(b + c) = ab + ac; that is, the monomial factor a is distributed, or separately applied, to each term of the binomial factor b + c, resulting in the product ab + ac.

Step-by-step explanation:

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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

Helen [10]

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):

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

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

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

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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.

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