1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
melamori03 [73]
3 years ago
6

Two triangles aresimilar.The length of a side of one of the triangle is 6times that of the corresponding sides of the other.Find

the ratio of the perimeter and the area of the triangle
Mathematics
1 answer:
GalinKa [24]3 years ago
6 0

Answer:

Ratio = 1 : 6 --- of perimeters

Ratio = 1: 36 --- of areas

Step-by-step explanation:

Given

Represent the sides of the first triangle with x, y and z

The sides of the second triangle will be 6x, 6y and 6z

Solving (a): Ratio of perimeter.

The perimeter of the first is:

P_1 = x + y + z

The perimeter of the second is:

P_2 = 6x +6 y + 6z

Factorize:

P_2 = 6(x +y + z)

The ratio is:

R = P_1 : P_2

R = x + y + z : 6(x + y + z)

Cancel out x + y + z

Ratio = 1 : 6

Solving (a): Ratio of Areas.

If the height of the first is h and the base is b.

The height of the second will be 6h and the base, 6b.

The area of the first is:

A_1 = 0.5 * b * h

A_1 = 0.5bh

The area of the second is:

A_2 = 0.5 * 6b * 6h

A_2 = 18b h

The ratio is:

Ratio = A_1 : A_2

Ratio = 0.5bh : 18bh

Divide by 0.5bh

Ratio = 1: 36

You might be interested in
Write the equation in slope-intercept form that contains the following point and is perpendicular to the given line
Len [333]

Answer:

y = 1/4 x -3

Step-by-step explanation:

y = -4x + 3;

the slope of this equation is -4

we want the slope perpendicular to this

take the negative reciprocal

- (-1/4) = 1/4

so the slope of our line will be 1/4

we have the slope and a point so we can use point slope form

y-y1 = m (x-x1)

y--2 = 1/4(x-4)

y+2 = 1/4 (x-4)

we need to change it to slope intercept form (y=mx+b)

distribute

y+2 = 1/4 x -1/4*4

y+2 = 1/4x -1

subtract 2 from each side

y +2-2 = 1/4 x -1-2

y = 1/4 x -3

the slope is 1/4 and the y intercept is -3

8 0
3 years ago
After five years of earning interest at an annual rate of 4%, an investment has earned $1,200 in interest. Determine the amount
Andru [333]
P=I÷rt
P initial investment ?
I interest earned 1200
R interest rate 0.04
T time 5 years

P=1,200÷(0.04×5)
P=6,000

Hope it helps
6 0
3 years ago
Read 2 more answers
A certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writin
Morgarella [4.7K]

Answer:

(a) We reject our null hypothesis.

(b) We fail to reject our null hypothesis.

(c) We fail to reject our null hypothesis.

Step-by-step explanation:

We are given that a certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hr.

A random sample of 18 pens is selected.

<u><em>Let </em></u>\mu<u><em> = true average writing lifetime under controlled conditions</em></u>

So, Null Hypothesis, H_0 : \mu \geq 10 hr   {means that the true average writing lifetime under controlled conditions is at least 10 hr}

Alternate Hypothesis, H_A : \mu < 10 hr    {means that the true average writing lifetime under controlled conditions is less than 10 hr}

<u>The test statistics that is used here is one-sample t test statistics;</u>

                           T.S. = \frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean

             s = sample standard deviation

             n = sample size of pens = 18

          n - 1 = degree of freedom = 18 -1 = 17

<u>Now, the decision rule based on the critical value of t is given by;</u>

  • If the value of test statistics is more than the critical value of t at 17 degree of freedom for left-tailed test, then <u>we will not reject our null hypothesis</u> as it will not fall in the rejection region.
  • If the value of test statistics is less than the critical value of t at 17 degree of freedom for left-tailed test, then <u>we will reject our null hypothesis</u> as it will fall in the rejection region.

(a) Here, test statistics, t = -2.4 and level of significance is 0.05.

<em>Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.</em>

Here, clearly the value of test statistics is less than the critical value of t as -2.4 < -1.74, so we reject our null hypothesis.

(b) Here, test statistics, t = -1.83 and level of significance is 0.01.

<em>Now, at 0.051 significance level, the t table gives critical value of -2.567 at 17 degree of freedom.</em>

Here, clearly the value of test statistics is more than the critical value of t as -2.567 < -1.83, so we fail to reject our null hypothesis.

(c) Here, test statistics, t = 0.57 and level of significance is not given so we assume it to be 0.05.

<em>Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.</em>

Here, clearly the value of test statistics is more than the critical value of t as  -1.74 < 0.57, so we fail to reject our null hypothesis.

8 0
3 years ago
Round each decimal to the nearest whole number
4vir4ik [10]

Answer:

1. 1

2. 8

3. 13

Step-by-step explanation:

hope that helps

6 0
2 years ago
sam divided a rectangle into 8 congruent rectangles that each have a area of 5 cm2. what is the area of the rectangle before it
Vikki [24]
Congruent= the same shape and size.

area of the rectangle before it is divided=8*(area congruent rectangle)
area of the rectangle before it is dividide=8*(5 cm²)=40 cm²

Area of the rectangle before it is dividide=40 cm²
5 0
3 years ago
Other questions:
  • Francisco is making an effort to drink more water, and has set a goal of 222 liters per day. He wants to know the volume of the
    15·1 answer
  • if it takes 30 steps to walk from the front of the store to the back and 40 steps to walk from the left of the store to the righ
    10·2 answers
  • How many weeks would it take Mai's family to finish 3 gallons of milk? Use one of the unit rates you found to solve.​
    13·1 answer
  • Which set of side lengths form a right triangle?
    14·2 answers
  • Median AM and CN of △ABC intersect at point O. What part of area of △ABC is the area of △AON?
    12·1 answer
  • Chloe collected 4 times as many bags of cans as her friend. If her friend college 1/6 of a bag, how much did Chloe collect?
    15·1 answer
  • What is the measure of angle DFG​
    6·1 answer
  • Seven times w is at least 21
    5·1 answer
  • What is the volume of this prism?
    6·1 answer
  • Hey guys, can someone help me with this, thank you ​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!