The perimeter of an airplane ticket is 30 centimeters. The area is 50 square centimeters. What are the dimensions of the ticket?

The length can be 5 and the width 10.

Step-by-step explanation:

perimeter is equal to 2L + 2W

area is equal to L * W

you get 2 equations:

30 = 2L + 2W

50 = L*W

we'll solve by substitution.

you can use either equation to solve for either variable.

we'll use the second equation to solve for L.

second equation is:

50 = L*W

divide both sides of this equation by W to get:

L = 50/W

we now have a value of L that we can substitute in the first equation which we can then use to solve for W.

the first equation is:

30 = 2L + 2W

replace L with 50/W to get:

30 = 2*(50/W) + 2W

simplify to get:

30 = 100/W + 2W

multiply both sides of this equation by W to get:

30W = 100 + 2W^2

subtract 30W from both sides of this equation to get:

2W^2 - 30W + 100 = 0

factor this equation to get:

(2W - 20) * (W - 5) = 0

solve for W to get:

W = 10 or W = 5

if W = 10, then use the equation of 50 = L*W to get L = 5

if W = 5, then use the equation of 50 = L*W to get L = 10

you have 2 possible solutions.

L = 5 and W = 10 or:

L = 10 and W = 5

both are plausible so we'll test them both out.

when L = 5 and W = 10:

the first equation becomes 2*5 + 2*10 = 10 + 20 = 30

the second equation becomes 5*10 = 50

both equations confirm that the solution of L = 5 and W = 10 is good.

when L = 10 andW = 5:

the first equation becomes 2*10 + 2*5 = 20 + 10 = 30

the second equation becomes 10*5 = 5

both equations confirm that the solution of L = 10 and W = 5 is good.

the ticket can have either:

a length of 5 and a width of 10 or:

a length of 10 and a width of 5.

since the length is usually longer than the width, you are free to choose that the ticket most likely has a length of 10 and a width of 5.

alternatively, you can simply say that the dimensions are 5 by 10 and let the recipient of that information determine which is the length and which is the width.

mathematically, the length can be 10 and the width 5 or the length can be 5 and the width 10.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

the answer is 0.3175 hope that you ^w^

also you might actually want to put this picture up if you want people to solve it luckily i remember this question