Answer:
4 feet by 8 feet
Explanation:
Given
[tex]P =24[/tex] -- Perimeter
[tex]A = 32[/tex] --- Area
Required
The dimension of the tent
The perimeter of a rectangle is:
[tex]P =2(L + W)[/tex]
Where
[tex]L = Length\\ W = Width[/tex]
So, we have:
[tex]2(L+W) = 24[/tex]
Divide both sides by 2
[tex]L + W = 12[/tex]
Make L the subject
[tex]L = 12 - W[/tex]
The area is calculated as:
[tex]A = L* W[/tex]
This gives:
[tex]L * W = 32[/tex]
Substitute[tex]L = 12 - W[/tex]
[tex](12 - W) * W = 32\\[/tex]
Open bracket
[tex]12W - W^2 = 32[/tex]
Express as quadratic equation
[tex]W^2 - 12W - 32 = 0[/tex]
Expand
[tex]W^2 - 8W -4W- 32 = 0[/tex]
Factorize
[tex]W(W - 8) -4(W- 8) = 0[/tex]
Factor out W - 8
[tex](W - 4)(W- 8) = 0[/tex]
Split
[tex]W - 4 = 0\ or\ W - 8 = 0[/tex]
Solve for W
[tex]W =4\ or\ W = 8[/tex]
Recall that:
[tex]L = 12 - W[/tex]
Substitute [tex]W =4\ or\ W = 8[/tex]
[tex]L = 12 - 4 = 8[/tex]
[tex]L = 12 - 8 = 4[/tex]
So, we have:
[tex]W =4\ or\ W = 8[/tex]
[tex]L = 8\ or\ L = 4[/tex]
So, the dimension is: 4 feet by 8 feet
