Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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 :

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

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

Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.