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3 years ago

A polygon has an area of 225 square meters. If the area is tripled, how does each side length change?

1 answer:

3 0

Let me tell you the process so that you get to the answer
Remember first that the area of a regular polygon with x sides has each of them a length which can be represented by y

A = 1/4 * xy^2 * Cot(180/x) 
The purpose is to solve for y, so we get 
y^2 = 4A/(xCot(180/x)) 
y = √(4A/(xCot(180/x)))

The thing we need to change is A in the previous formula and with that we can use the equaation to be a constant. This could be represented by Z
Z = √(4/(xCot(180/x)))
so
Y = Z√A
If we increase area by a factor s, y increases by a factor of √x.
So if you want to know the triple then you need to increase it by √3

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Given sin A = 12/13 and that angle A is in Quadrant 1,

UkoKoshka [18]

We have been given that $\text{sin}(A)=\frac{12}{13}$ and angle A is in quadrant 1. We are asked to find the exact value of $\text{cot}(A)$ in simplest radical form.

We know that sine relates opposite side of right triangle with hypotenuse.

$\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}$

This means that opposite side is 12 units and hypotenuse is 13 units.

We know that cotangent relates adjacent side of right triangle with adjacent side.

$\text{cot}=\frac{\text{Adjacent}}{\text{Opposite}}$

Now we will find adjacent side using Pythagoras theorem as:

$\text{Adjacent}^2=\text{Hypotenuse}^2-\text{Oppoiste}^2$

$\text{Adjacent}^2=13^2-12^2$

$\text{Adjacent}^2=169-144$

$\text{Adjacent}^2=25$

Let us take positive square root on both sides:

$\sqrt{\text{Adjacent}^2}=\sqrt{25}$

$\text{Adjacent}=5$

Therefore, adjacent side of angle A is 5 units.

$\text{cot}(A)=\frac{5}{12}$

Therefore, the exact value of cot A is $\frac{5}{12}$ .

5 0

3 years ago

Hari borrowed Rs. 126000 from a money-lender at 15% per annum simple interest,

amid [387]

Answer:

Rs. 112000

Step-by-step explanation:

Borrowed money = Rs. 126000
Interest rate = 15% PA simple
Time = 3 years

Hari is due to pay after 3 years:

126000* (1+ 3*15/100) = 182700

He pays Rs. 70700, remaining money is cleared by giving buffalo.

Cost of buffalo:

182700 - 70700= Rs. 112000

Answer is: Rs. 112000

7 0

3 years ago

Read 2 more answers

A line joins the point

Harrizon [31]

Intersection of the first two lines:

$\begin{cases}5x - 2y + 3 = 0\\4x - 3y + 1 = 0\end{cases}$

Multiply the first equation by 4 and the second by 5:

$\begin{cases}20x - 8y + 12 = 0\\20x - 15y + 5 = 0\end{cases}$

Subtract the two equations:

$(20x - 8y + 12)-(20x - 15y + 5)=0 \iff 7y+7=0 \iff y=-1$

Plug this value for y in one of the equation, for example the first:

$5x - 2\cdot (-1) + 3 = 0\iff 5x+5=0 \iff x=-1$

So, the first point of intersection is $(-1,-1)$

We can find the intersection of the other two lines in the same way: we start with

$\begin{cases}x=y\\x=3y+4\end{cases}$

Use the fact that x and y are the same to rewrite the second equation as

$x=3x+4 \iff 2x=-4 \iff x=-2$

And since x and y are the same, the second point is $(-2, -2)$

So, we're looking for a line passing through $(-1,-1)$ and $(-2, -2)$ . We may use the formula to find the equation of a line knowing two of its points, but in this case it is very clear that both points have the same coordinates, so the line must be $y=x$

In the attached figure, line $5x - 2y + 3 = 0$ is light green, line $4x - 3y + 1 = 0$ is dark green, and their intersection is point A.

Simiarly, line $x=y$ is red, line $x = 3y + 4$ is orange, and their intersection is B.

As you can see, the line connecting A and B is the red line itself.

5 0

3 years ago

a rectangular corn hole area at the recreation center has a width of 5 feet and a length of 10 feet. if a uniform amount is adde

harkovskaia [24]

Let
x-------------> amount added to each side
A-------------> area increased----------> 84 ft²

we know that
A=(10+x)*(5+x)=84-----------> 10*5+10*x+5*x+x²
50+15x+x²=84----------> x²+15x-34=0
solving the second order equation
x1=-17
x2=2

the answer is x=2 ft

3 0

3 years ago

Read 2 more answers

A yield sign measures 30 inches on all three sides. what is the area of the sign

Nookie1986 [14]

Answer:

450

Step-by-step explanation:

To find an area of the triangle, you must first multiply the base and the height.

5 0

3 years ago