Answered

Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

A new ice skating rink will be approximately rectangular in shape and will have an area of 19,720 square feet. Using an equation for the perimeter P, of the skating rink in terms of its width W, what are the dimensions of the skating rink if the perimeter is 634 feet?


The dimensions of the rink are ? feet by ? feet.

Sagot :

MrRoyal

Answer:

The dimension is: 232ft by 85ft

Step-by-step explanation:

Given

Shape: Rectangle

[tex]A = 19720[/tex] --- Area

[tex]P = 634[/tex] --- Perimeter

Required

Determine the dimension

Area is calculated as:

[tex]A = L * W[/tex]

This gives

[tex]19720 = L * W[/tex]

Perimeter is calculated as:

[tex]P = 2(L + W)[/tex]

This gives

[tex]634 = 2(L + W)[/tex]

Divide both sides by 2

[tex]317 = L + W[/tex]

Make L the subject

[tex]L = 317 -W[/tex]

Substitute 317 - W for L in [tex]19720 = L * W[/tex]

[tex]19720 = (317 - W)*W[/tex]

Open brackets

[tex]19720 = 317W - W^2[/tex]

Rewrite as:

[tex]W^2 - 317W + 19720 = 0[/tex]

Expand

[tex]W^2 -232W - 85W + 19720 = 0[/tex]

Factorize:

[tex]W(W -232) - 85(W - 232)= 0[/tex]

[tex](W - 85) (W - 232)= 0[/tex]

Split

[tex]W = 85\ or\ W = 232[/tex]

Recall that:

[tex]L = 317 -W[/tex]

[tex]L= 317 - 85\ or\ L = 317 - 232[/tex]

[tex]L= 232\ or\ L = 85[/tex]

Hence, the dimension is: 232ft by 85ft

abidemiokin

The dimension of the  rectangular rink is 85ft by 232ft

Perimeter and Areas of triangle

Given the following parameters

  • Area = 19,720 square feet.
  • Perimeter = 634 feet

The formula for finding the area is:

A = lw

lw = 19,720

l = 19,720/w

If the perimeter is 634 feet

2(l+w) = 634

2(19,720/w + w) = 634

39,440/w + 2w = 634

39,440 + 2w^2 = 634w

2w^2 - 634w + 39,440 = 0

On factorizing, w=85 or w=232

Since l = 19,720/w

l = 19,720/232

l = 85

Hence the dimension of the  rectangular rink is 85ft by 232ft

Learn more on area of triangle here: https://brainly.com/question/17335144

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.