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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
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