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andrew11 [14]
3 years ago
14

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AC =16 and DC=5 what is the length of BC in the simplest ra

dical form

Mathematics
1 answer:
Nana76 [90]3 years ago
7 0

The length of BC is 4 \sqrt{5}.

Solution:

Given ABC is a right triangle.

AC is the hypotenuse and BD is the altitude.

AB and BC are legs of the triangle ABC.

AC = 16 and DC = 5

<u>Leg rule of geometric mean theorem:</u>

$\frac{\text { hypotenuse }}{\text { leg }}=\frac{\text { leg }}{\text { part }}$

$\Rightarrow \frac{AC}{BC}=\frac{BC}{DC}$

$\Rightarrow \frac{16}{x}=\frac{x}{5}$

Do cross multiplication.

\Rightarrow  16\times 5 = x\times x

\Rightarrow  80= x^2

\Rightarrow  16\times 5= x^2

Taking square root on both sides.

\Rightarrow  \sqrt{16\times 5} = \sqrt{x^2}

\Rightarrow  \sqrt{4^2\times 5} = \sqrt{x^2}

square and square roots get canceled, we get

\Rightarrow  4\sqrt{ 5} = x

The length of BC is 4 \sqrt{5}.

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(-3,3] is an interval which means that -3 and 3 are not inclusive of the values of x -5/3.

We have given

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2 years ago
The length of a rectangle 8 more than the width .the area is 513 square inches .find the length and width of the rectangle
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Step-by-step explanation:

Let width be w inches so according to given scenario as length is 8 more than width so the equation becomes

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