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MariettaO [177]
2 years ago
12

An equilateral triangle has a perimeter of 48 cm. What is the area?

Mathematics
1 answer:
KiRa [710]2 years ago
6 0

Answer:

A=64\sqrt{3}\ cm^2

Step-by-step explanation:

we know that

An <u><em>equilateral triangle</em></u> has three equal sides and three equal interior angles (each interior angle measure 60 degrees)

so

The perimeter is equal to

P=3b

where

b is the length side of the equilateral triangle

we have

P=48\ cm

substitute

48=3b

solve for b

b=48/3\\b=16\ cm

Find the area

The formula of area applying the law of sines is equal to

A=\frac{1}{2}b^2sin(60^o)

substitute the value of b

A=\frac{1}{2}(16)^2sin(60^o)

sin(60^o)=\frac{\sqrt{3}}{2}

A=\frac{1}{2}(16)^2(\frac{\sqrt{3}}{2})

A=64\sqrt{3}\ cm^2

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A rectangle has a width of x centimeters and a perimeter of 8x centimeters a square has sides of length 1/4 that of the length o
Amanda [17]

Answer:

Part A) The length of rectangle is 3x\ cm

Part B) The perimeter of the square is 3x\ cm

Part C) 20\ cm

Part D) 39\ cm^{2}

Step-by-step explanation:

Part A) Find the length of the rectangle

we know that

The perimeter of rectangle is equal to

P=2(L+W)

we have

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substitute and solve for L

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L=4x-x=3x\ cm

Part B) Find the perimeter of the square

we know that

The perimeter of a square is

P=4b

we have that

b=(1/4)L

substitute the value of L

b=(1/4)3x=(3/4)x\ cm

Find the perimeter of the square

P=4(3/4)x=3x\ cm

Part C) Find how many cm greater the rectangle's perimeter than the square's perimeter if x=4

<u>Find the value of rectangle's perimeter</u>

P=8x\ cm ------> P=8(4)=32\ cm

<u>Find the value of square's perimeter</u>

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<u>Find the difference</u>

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<u>Find the value of rectangle's area</u>

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<u>Find the value of square's area</u>

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<u>Find the difference</u>

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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