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3 years ago

In the figure below, BD bisects ∠ABC. What is the length of AB?

Mathematics

1 answer:

dimaraw [331]3 years ago

3 0

Answer:

D. 12

Step-by-step explanation:

Based on the Angle Bisector theorem, the opposite sides of ∆ABC are divided into proportional segments alongside the two other sides of the triangle, as BD bisects the <ABC. This implies that:

AB/AD = CB/CD

Substitute

AB/8 = 6/4

Cross multiply

AB*4 = 6*8

AB*4 = 48

AB = 48/4

AB = 12

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Which of the following is not a correct name for the line shown?

Talja [164]

Answer:

Step-by-step explanation:

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Consider all options:

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B. Points W and X lie on the line, so you can name the line as WX (true option)

C. p represents the line (small letter given on the diagram) - (true option)

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3 years ago

The perimeter of an equilateral triangle is 12\/3 cm. Find the radius, apothem and area of the equilateral triangle.

Irina-Kira [14]

Answer:

Radius - 4

Apothem - 2

Area - $12\sqrt{3}$ or 20.8

Step-by-step explanation:

Try to draw out my explanation so you know what this looks like.

~~~~

This is an equilateral triangle, so all sides are the same length. The perimeter can be divided by 3 to get each side length...

$12\sqrt{3} \div3 = 4\sqrt{3}$

Now that we know the side lengths, we can get this started!

~~~~

Now, an equilateral triangle has angles that all equal 60 degrees. We can bisect this into TWO special case triangles of measures 90-60-30.

4 times the square root of 3 will be the hypotenuse, and the smallest leg is always half of that. The larger leg is represented as the small leg times the square root of 3.

$Small=2\sqrt{3} \\Hypotenuse = 4\sqrt{3} \\Long =6$

By the way, the formula for the area can be either of the two:

$A= \frac{1}{2} bh\\or\\A = \frac{1}{2} NAS$

we can easily find the area using the first formula.

$A= \frac{1}{2} (4\sqrt{3} )(6)\\A=12\sqrt{3}$

The radius is the distance from the center to the corners & the apothem is the distance from the center to a side...

So we can divide the big triangle into a mini triangle at the bottom left/right

The height (small leg) of that triangle would be the apothem

The hypotenuse of that triangle would be the radius.

I did the math really quick because this is getting long. Anyhow, the small leg is 2 so is the apothem, and the hypotenus is 4, so is the radius

Happy April Fool's btw, lol.

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