A rectangular tent has a perimeter of 24 feet. Its area is 32 square feet. What are the dimensions of the tent?

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

Answer quick please I’ll give you brainliest.

1. Based on your knowledge of world history, which of the following contributed LEAST to
environmental changes in the twentieth century?
a. The growth of regional trading blocs in the late twentieth century
b. Development of heavy
industry by communist governments in the Soviet Union and China
c. Increased population growth as a result of scientific breakthroughs
d. The globalization of consumer culture