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galina1969 [7]
3 years ago
15

Given an equilateral triangle that has an area of 1959 cm2. What is the length of its sides?

Mathematics
1 answer:
Nina [5.8K]3 years ago
7 0
Equilateral
equi means equal
lateral means sides

all sides are equal
triangle has 3 sides

perimiter=side1+side2+side3
side1=side2=side3


area=1/2 times base times height
base=side
draw a line down the middle of te tiangle so you get 2 right triangles side by side
1/2base is one leg
base is hypotonuse
height is unknown
equilateral means that it is a 30-60-90 triangle with  hypotonuse equal to 2x, height=x√3, bottom is x
1/2 times base times height=1959
1/2 times x times x√3=1959
multiply both sides by 2
(x^2)√3=3918
divide both sides by √3
x^2=3918/√3
square root both sides
x=47.5611
side=hypotonuse=2x
2x=2*47.5611
side=95.12222


legnth of each side is 2\sqrt{ \frac{3918}{ \sqrt{3} } }cm or about 95.12222 cm
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<h3>Answer:  Trapezoid</h3>

==========================================================

Explanation:

There are two ways to do this problem.

Method 1 involves listing out the terms until we reach the seventh one.

  1. square
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We see that the trapezoid is term 7.

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Method 2 is faster and the one I recommend.

Since the pattern repeats every 4 items, this means we divide by 4 and look at the remainder. Ignore the quotient entirely.

7/4 = 1 remainder 3

The remainder 3 means that the answer is found in term 3, which is the trapezoid.

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Step-by-step explanation:

The maximum or minimum of a quadratic function occurs at

x

=

−

b

2

a

. If

a

is negative, the maximum value of the function is

f

(

−

b

2

a

)

. If

a

is positive, the minimum value of the function is

f

(

−

b

2

a

)

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f

min

x

=

a

x

2

+

b

x

+

c

occurs at

x

=

−

b

2

a

Find the value of

x

equal to

−

b

2

a

.

x

=

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b

2

a

Substitute in the values of

a

and

b

.

x

=

−

−

12

2

(

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Remove parentheses.

x

=

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−

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2

(

2

)

Simplify

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−

12

2

(

2

)

.

Tap for more steps...

x

=

3

The maximum or minimum of a quadratic function occurs at

x

=

−

b

2

a

. If

a

is negative, the maximum value of the function is

f

(

−

b

2

a

)

. If

a

is positive, the minimum value of the function is

f

(

−

b

2

a

)

.

f

min

x

=

a

x

2

+

b

x

+

c

occurs at

x

=

−

b

2

a

Find the value of

x

equal to

−

b

2

a

.

x

=

−

b

2

a

Substitute in the values of

a

and

b

.

x

=

−

−

12

2

(

2

)

Remove parentheses.

x

=

−

−

12

2

(

2

)

Simplify

−

−

12

2

(

2

)

.

Tap for more steps...

x

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