Plz help urgent question below

A square park measures 170 feet along each side. Two paved paths run from each corner to the opposite corner and extend 3 feet i

Cerrena [4.2K]

Answer:

The total area, in square feet, taken by the paths is 2,004

Step-by-step explanation:

see the attached figure with lines to better understand the problem

I can divide the figure into four right triangles, one small square and four rectangles

step 1

Find the area of the right triangle of each corner of the path

The area of the triangle is

$A=(1/2)(b)(h)$

substitute the given values

$A=(1/2)(3)(3)=4.5\ ft^2$

step 2

Find the hypotenuse of the right triangle

Applying Pythagoras Theorem

Let

d -----> hypotenuse of the right triangle

$d^{2}=3^{2}+3^{2}$

$d^{2}=18$

$d=\sqrt{18}\ ft$

simplify

$d=3\sqrt{2}\ ft$

The hypotenuse of the right triangle is equal to the width of the path

step 2

Find the area of the small square of the path

The area is

$A=b^{2}$

we have

$b=3\sqrt{2}\ ft$ ----> the width of the path

substitute

$A=(3\sqrt{2})^{2}$

$A=18\ ft^2$

step 3

Find the length of the diagonal of the square park

Applying Pythagoras Theorem

Let

D -----> diagonal of the square park

$D^{2}=170^{2}+170^{2}$

$D^{2}=57,800$

$D=\sqrt{57,800}\ ft$

simplify

$D=170\sqrt{2}\ ft$

step 4

Find the height of each right triangle on each corner

The height will be equal to the width of the path divided by two, because is a 45-90-45 right triangle

$h=1.5\sqrt{2}\ ft$

step 5

Find the area of each rectangle of the path

The area of rectangle is $A=LW$

we have

$W=3\sqrt{2}\ ft$ ----> width of the path

Find the length of each rectangle of the path

$L=(D-2h-d)/2$

where

D is the diagonal of the park

h is the height of the right triangle in the corner

d is the width of the path (length side of the small square of the path)

substitute the values

$L=(170\sqrt{2}-2(1.5\sqrt{2})-3\sqrt{2})/2$

$L=(170\sqrt{2}-3\sqrt{2}-3\sqrt{2})/2$

$L=(164\sqrt{2})/2$

$L=82\sqrt{2}\ ft$

Find the area of each rectangle of the path

$A=LW$

we have

$W=3\sqrt{2}\ ft$

$L=82\sqrt{2}\ ft$

substitute

$A=(82\sqrt{2})(3\sqrt{2})$

$A=492\ ft^2$

step 6

Find the area of the paths

Remember

The total area of the paths is equal to the area of four right triangles, one small square and four rectangles

so

substitute

$A=4(4.5)+18+4(492)=2,004\ ft^2$

therefore

The total area, in square feet, taken by the paths is 2,004

3 0

3 years ago

On a blueprint, an architect drew a 12 inch line to represent the length of a 30-foot room. If the line that represents the widt

mash [69]

Answer:

20 ft

Step-by-step explanation:

30 ft/ 12 inches= 2.5ft/in x 8 in= 20 ft

I hope this helps and good luck!

6 0

3 years ago

Given that (4,-7 is on the graph of f(x), find the corresponding point for the function f(x)+4

alexandr402 [8]

Answer:

The corresponding point for the function f(x)+4 would be (4,-3)

Step-by-step explanation:

Since the transformation is outside of the parenthesis, that means the y-coordinate is only affected.

add 4 to -7 and you get -3

5 0

3 years ago

Find the common ratio of the geometric sequence 18,-90,450,...

svetlana [45]

Answer:

try looking it up on socratic

3 0

3 years ago

Read 2 more answers

A side of a square is 10 m longer than the side of an equilateral triangle the perimeter of the square is three times the perime

Slav-nsk [51]

Answer:

$\large \boxed{\text{8 m}}$

Step-by-step explanation:

Let side of triangle = x

And side of rectangle = y

Perimeter of triangle = 3x

Perimeter of rectangle = 4y

We have two conditions:

$\begin{array}{lrcl}(1) & y & = & x + 10\\(2) &4y & = & 3\times 3x\\& 4y & = & 9x\\& 4(x + 10) & = & 9x\\& 4x + 40 & = & 9x\\& 40 & = & 5x\\& x& = &\mathbf{8}\\\end{array}\\\text{Each side of the triangle is $\large \boxed{\textbf{8 m}}$ long.}$

3 0

3 years ago