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2 years ago

Find the area of the equilateral triangle

Mathematics

2 answers:

uranmaximum [27]2 years ago

8 0

Answer:

Step-by-step explanation:

Suppose that the side length is s. Imagine that one side is level. Draw a vertical line through the top vertex perpendicular to the base (level side). Label this vertical line "h." Then h and s are related as follows:

√3 h

sin 60 degrees = ------- = --------

2 s

s√3

and so h = the height of the triangle = -----------

The area of this triangle is (1/2)(base)(height), which here is:

(1/2)(s/2)( s√3 /2), or

(s^2)√3

A = ---------------

dezoksy [38]2 years ago

6 0

Is there supposed to be a picture of the triangle?

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A rectangle sand box has a length of 5 and 1/3 feet and a width of 3 and 3/4 feet. What is the perimeter?

Varvara68 [4.7K]

Answer:

Perimeter of rectangle = ⇒ $18\frac{1}{6}$ feet

Step-by-step explanation:

Given:

Length of a rectangular sand box = $5\frac{1}{3}\ feet$

Width of the box = $3\frac{3}{4}\ feet$

Perimeter of a rectangle = $2(l+w)$

where $l$ represents length of rectangle and $w$ represents width of the rectangle.

Substituting values given for length and width.

Perimeter of sand box = $2(5\frac{1}{3}+3\frac{3}{4})\ feet$

Simplifying by adding fractions:

⇒ $2(5+3+\frac{1}{3}+\frac{3}{4})\ feet$ (Adding whole numbers and fractions separately)

⇒ $2(8+\frac{1}{3}+\frac{3}{4})$ feet

Whole number 8 can be written as $\frac{8}{1}$

⇒ $2(\frac{8}{1}+\frac{1}{3}+\frac{3}{4})$ feet

To add fractions we take LCD for the denominators 3,4,1.

LCD for 3 and 4 = 12 as its the least common multiple of 3,4,1.

Making denominators =12 by multiplying numerator an denominator with the corresponding numbers

⇒ $2(\frac{8\times 12}{1\times 12}+\frac{1\times 4}{3\times 4}+\frac{3\times 3}{4\times 3})$ feet

⇒ $2(\frac{96}{12}+\frac{4}{12}+\frac{9}{12})$ feet

Then we simply add numerators.

⇒ $2(\frac{96+4+9}{12})$ feet

⇒ $2(\frac{109}{12})$ feet

⇒ $2\times \frac{109}{12}$ feet

⇒ $\frac{218}{12}$ feet

Writing fraction as a mixed number by dividing 218 by 12 and writing quotient as whole number and remainder as numerator with divisor as denominator.

⇒ $18\frac{2}{12}$ feet

Simplifying fractions to simplest form.

⇒ $18\frac{1}{6}$ feet

Perimeter =⇒ $18\frac{1}{6}$ feet (Answer)

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3 years ago

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Kaylis [27]

Answer:

$3.72

Step-by-step explanation:

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Hope this helps!

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2 years ago

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Answer:

The t-distribution is used.

Step-by-step explanation:

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3 years ago

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