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jenyasd209 [6]
3 years ago
7

The area of two similar triangles are 50dm^2 and 32dm^2. The sum of their perimeters is 117dm. What us the perimeters of each of

these triangle?
Mathematics
1 answer:
Kay [80]3 years ago
5 0

Answer:

Perimeter of one triangle is 65 dm

Perimeter of other triangle is 52 dm

Step-by-step explanation:

Please remember the concept

If sides are in the ratio of a:b

Then the area in the ratio of a^{2} :b^{2}

It is given sum of their perimeter is 117.

Let the small triangle has perimeter as x.

So, perimeter of big triangle is 117-x.

So, we can set up equation as

\frac{50}{32} =\frac{x^{2} }{(117-x)^{2} }

Cross multiply

50(117-x)^2 =32x^2

Expand the left side

50(13689 -234x+x^{2} )=32x^{2}

Distribute the left side

684450-11700x+50x^{2}=32x^{2}

Subtract both sides 32x^{2} and rewrite it 18x^{2} -11700x+684450=0

Solve this quadratic for x.

Divide both sides of the equation by 18 to simplify.

x^{2}-650 x+38025=0

Now, if possible let's factor

Find two integers whose multiplication is 38025 but adds to -650.

-65 and -585 works.

So, we can rewrite it as

(x -65)(x-585) =0

Solve them using zero product property

x=65, x=585

So, x=65 works here.

So, perimeter of one triangle is 65 dm

Perimeter of other triangle is 117-65= 52 dm

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2n + 1.6 = 17.6 what is the value of n?​
Vinil7 [7]

Answer:

<h2><u><em>n = 8</em></u></h2>

Step-by-step explanation:

2n + 1.6 = 17.6 what is the value of n?​

2n + 1.6 = 17.6

2n = 17.6 - 1.6

2n = 16

n = 16 : 2

n = 8

-----------------

check

2n + 1.6 = 17.6

2*8+1.6=17.6

16+1.6=17.6

17.6=17.6

the answer is good

7 0
2 years ago
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A map has a scale of 1 cm to 20km. Rewrite the scale as a ration in its simplest form.
Lesechka [4]

Answer:

1 : 2000000

Step-by-step explanation:

we have to convert 20km into cm so

20km×100000

=2000000

So ratio is 1:2000000

<h2>MARK ME BRAINLIEST PLS!</h2>
6 0
2 years ago
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Mrs.Barkley has 75 feet ribbon. If each of the 18 students in her class gets an equal length of ribbon, how many inches of ribbo
Black_prince [1.1K]

Answer:

Each student would get 4 inches of ribbon


Step-by-step explanation:

Mrs. Barkley has 75 inches of ribbon and is splitting it between 18 students so you would divide 75 by 18. When you divide you get 4.166666... etc. So the answer would be 4

3 0
3 years ago
Gerald has a punch bowl in the shape of a hemisphere as shown below.
zmey [24]

The closest to the maximum number of cups the punch bowl can hold is 30

<h3>How to determine the number of cups?</h3>

The given parameters are:

1 cup = 15 cubic inches

Diameter of bowl, d = 12 inches

The radius is the half of the diameter.

So, we have:

r = 6

The volume of the bowl is then calculated using:

V = \frac{2}{3}\pi r^3

This gives

V = \frac{2}{3}\pi * 6^3

Evaluate

V = 452.16

The maximum number of cups is then calculated using:

Cups = 452.16/15

Evaluate

Cups = 30.1444

Approximate

Cups = 30

Hence, the closest to the maximum number of cups the punch bowl can hold is 30

Read more about volumes at:

brainly.com/question/1972490

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6 0
2 years ago
In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD=√2 cm.
Zielflug [23.3K]

Given that triangle ABC is right angle triangle. CD is altitude such that AD=BC

ABC is a right angle triangle so apply Pythogorean theorem

AC^{2} + BC^{2} = AB^{2}

AC^{2} + AD^{2} = AB^{2}      (Given that AD = BC)

AC^{2} + AD^{2} = 3^{2}      (Given that AB=3)

AC^{2} + AD^{2} = 9 ...(i)

ADC is a right angle triangle so apply Pythogorean theorem

AD^{2} + CD^{2} = AC^{2}

AD^{2}+(\sqrt{2})^2= AC^{2}

AD^{2}+2= AC^{2}

AD^{2}=AC^{2} -2 ...(ii)


Plug value (ii) into (i)

AC^{2} + AC^{2}-2 = 9

2AC^{2} -2=9

2AC^{2} =11

AC^{2} =\frac{11}{2}

AC=\sqrt{\frac{11}{2} }


Hence final answer is AC=\sqrt{\frac{11}{2} }

8 0
3 years ago
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