MATHEMATICS MIDDLE SCHOOL

Rectangle with a side length of 11" and a diagonal of 14" what is the perimeter

Answers

Answer 1

Answer:

Hello!

The answer is:

The perimeter of the rectangle is equal to 39.32".

$Perimeter=39.32in$

Why?

Since we are working with a rectangle, we can use the Pythagorean theorem to find the missing side of the rectangle and calculate its perimeter. We must remember that we can divide a rectangle into two equal right triangles.

According to the Pythagorean Theorem, we have:

$a^(2)=b^(2)+c^(2)$

Where:

a, represents the hypotenuse of the triangle which is equal to the diagonal of the given rectangle (14")

b and c are the other sides of the triangle.

Now, let be "a" 14" and "b" 11"

So, solving we have:

$a^(2)=b^(2)+c^(2)$

$14^(2)=11^(2)+c^(2)$

$14^(2)-11^(2)=c^(2)$

$14^(2)-11^(2)=c^(2)\n\nc=\sqrt{14^(2) -11^(2) }=√(196-121)=√(75)=8.66in$

Now, that we already know the the missing side of the rectangle, we can calculate the perimeter using the following formula:

$Perimeter=2base+2length\n\nPerimeter=2*11in+2*8.66in=22in+17.32in=39.32n$

Hence, we have that the perimeter of the rectangle is equal to 39.32".

Have a nice day!

Answer 2

Answer:

Answer:

10sqrt3+22

Step-by-step explanation:

Ok, let us imagine it as a sort of rectangle split upon its diagonal.

Using that, we can Pythag it out,

11^2+b^2=14^2

121+b^2=196

b^2=75

b=sqrt75

b=5sqrt3

Ok, using this info, we find the perimeter,

5sqrt3+5sqrt3+11+11

10sqrt3+22

The answer is 10sqrt3+22

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A painter has a 24-foot ladder that he is using to paint a house. For safety reasons, the ladder must be placed at least 8 feet from the base of the side of the house. To the nearest tenth of a foot, how high can the ladder safely reach?

Answers

pythagorean theorem
legnth of lader is hypotonuse (leaning against wall and wall is one leg and distance from wall to bottom of ladder is other leg)

so
a^2+b^2=c^2 where a and b are legs and c=hypotonuse

a=8

c=24
8^2+b^2=24^2
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subtract 64
b^2=512
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22.6

answer is 22.6 ft

Latoya needs 2 gallons of juice to make a fruit punch for an event, but she only has a measuring cup. She knows there are 4 quarts in 1 gallon, 2 pints in 1 quart, and 2 cups in 1 pint. How many cups of juice does she need to make 2 gallons?

Answers

Answer:

32 cups of juice Latoya need to make 2 gallons .

Step-by-step explanation:

As given

Latoya needs 2 gallons of juice to make a fruit punch for an event, but she only has a measuring cup .

Latoya knows that there are

4 quarts = 1 gallon

2 pints = 1 quart

2 cups = 1 pints

As take

2 cups = 1 pints

Multiply above by 2 on both sides .

4 cups = 2 pints ( As 2 pints = 1 quart )

Thus

4 cups = 1 quarts

Multiply the above by 4 on both sides.

Thus

16 cups = 4 quarts (As 4 quarts = 1 gallon)

Thus

16 cups = 1 gallon

Now calculate how much gallons of juice contain by 1 cups.

$Gallons\ of\ juice\ contain\ by\ 1\ cups = (1)/(16)\ gallons$

Let us assume that the number of cups of juice does Latoya need to make 2 gallons be x.

Than

$(1* x)/(16) = 2$

x = 16 × 2

x = 32 cups

Therefore 32 cups of juice Latoya need to make 2 gallons .

Latoya would need 32 cups of juice to make 2 gallons.

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Answers

40.000+9.000+5.00+6.0+4. maybe good luck

What is 9/2 as a decimal

Answers

4.5 :) is the correct answer

The answer would be 4.5

Tara has two standard, six-sided dice. If she rolls them 36 times, how many times should she expect a sum less than 5 to show up? Justify your answer.

Answers

There are six sides on each die. For each possible score on Die 1, there are six possible scores on Die 2. So the number of possible combinations is 6*6 = 36.
It follows that if the dice are thrown 36 times, you would expect each combination to come up once.

We therefore simply need to know how many combinations add up to less than 5. (I've interpreted this as not including a total of 5 itself).
These combinations are: 1 and 1, 2 and 1, 1 and 2, 2 and 2, 3 and 1, and 1 and 3 ---> six combinations out of 36.

So you'd expect a sum less than 5 six times.

What is 3c+2(2c+5)=3 solveWhat is d-15.6=2d-556.3 solve
What is 9b-10=2(3b+4) solve
Please help me 20 points

Answers

Answer:

3c+2(2c+5)=3 c= -1

d-15.6=2d-556.3 d=540.7

9b-10=2(3b+4) b=6

Step-by-step explanation:

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