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3 years ago

An equilateral triangle has an apothem of 5 cm. Find the perimeter of the triangle to the nearest centimeter.

1 answer:

4 0

The apothem is the distance from the center to the midpoint of one of the sides of a regular polygon. You can make a right triangle with the apothem, the line from the midpoint to the corner and the line from the center to the corner. An equilateral triangle has 60 degree angles (180/3). The right triangle has half of one of those angles so 30 degrees. Now we have a 30-60-90 triangle where the short leg is 5cm. The long leg, which is also half of one side of the triangle is thus $5\sqrt{3}$ . A whole side of the triangle is $10\sqrt{3}$ . Multiply that by 3 to get the perimeter of $30\sqrt{3}$ .

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RS=2x-8, ST = 11, RT = x+10

ziro4ka [17]

Answer:

$Equation~=~\Large\boxed{2x+3=x+10}$

$x~=~\Large\boxed{7}$

$RS~=~\Large\boxed{6}$

$RT~=~\Large\boxed{17}$

Step-by-step explanation:

Given information

$RS=2x-8$

$ST=11$

$RT=x+10$

Derived expression from the given information

Presumably, I think this is a combination of segments

$RS+ST=RT$

Substitute values into the given expression

$(2x-8)+(11)=(x+10)$

Combine like terms

The following is the expression

$\Large\boxed{2x+3=x+10}$

Subtract 3 on both sides

$2x+3-3=x+10-3$

$2x=x+7$

Subtract x on both sides

$2x-x=x+7-x$

$\Large\boxed{x=7}$

Substitute the x value into corresponding expressions to determine the final value

$RS=2x-8=2(7)-8=14-8=\Large\boxed{6}$

$RT=x+10=(7)+10=\Large\boxed{17}$

Hope this helps!! :)

Please let me know if you have any questions

3 0

2 years ago

Write the expression 18 - 27-9 in the form of a +bi.

My name is Ann [436]

V(18-1811) también eres el mejor en la vida y tú me ganas de comer

3 0

3 years ago

Can a table still be a function if the x values arent the same but 2 y values are the same?

Contact [7]

The answer is yes.

Its yes because it exactly one input(x) & multi outputs(y).

5 0

3 years ago

WILL GIVE 10 POINTS Leona was using an eyedropper to place droplets in a small container.

il63 [147K]

Answer:

A. milliliters B. 8 fluid ounces

Step-by-step explanation:

An eyedropper is very small and can only hold a small amount. You can eliminate 2 from the start: millimeter and meter. These two are use for measuring distance not volume. ex.) I walked 2 meters. A liter is too big for an eyedropper. ex.) 1 liter of soda.

A glass full of juice would be 8 fuild ounces because a glass is basically a cup. A 8 gallons is too big, and a 8 tablespoons is too small. ex.) gallon of milk and tablespoon of sugar. 8 cups is too big because a glass is about 1 cup. 8 fluid ounces = 1 cup

4 0

3 years ago

Two streets bounding your triangular lot make an angle of 74∘. The lengths of the two sides of the lot on these streets are 126

ycow [4]

Answer: a) Yes, there is enough fance

b) 58.1° and 47.9°

c) The city will not approve, because 1/3 of the area is just 2220.5ft²

Step-by-step explanation:

a) using law of cosines: x is the side we do not know.

x² = 126² + 110² - 2.126.110.cos74°

x² = 20335.3

x = 142.6 ft

So 150 > 142.6, there is enough fance

b) using law of sine:

sin 74/ 142.6 = sinα/126 = sinβ/110

sin 74/ 142.6 = sinα/126

0.006741 = sinα/126

sinα = 0.849

α = sin⁻¹(0.849)

α = 58.1°

sin 74/ 142.6 = sinβ/110

0.006741 = sinβ/110

sinβ = 0.741

β = sin⁻¹(0.741)

β = 47.9°

Checking: 74+58.1+47.9 = 180° ok

c) Using Heron A² = p(p-a)(p-b)(p-c)

p = a+b+c/2

p=126+110+142.6/2

p=189.3

A² = 189.3(189.3-126)(189.3-110)(189.3-142.6)

A = 6661.5 ft²

1/3 A = 2220.5

So 2300 > 2220.5. The area you want to build is bigger than the area available.

The city will not approve

7 0

3 years ago