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Alenkasestr [34]
3 years ago
11

A teacher runs a total of 48 city blocks in a rectangular pattern. If the width of the run is 3x and the length of the run is 5x

+ 4, what is the perimeter of the path the teacher runs? all you have to do is a equation don't solve it :)
Mathematics
1 answer:
Ghella [55]3 years ago
6 0

Answer:

P = 16x + 8

Step-by-step explanation:

Perimeter of a rectangle

= 2(L + W)

Given

L = 5x + 4 and

W = 3x

Therefore

Perimeter = 2(5x + 4 + 3x)

Rearrange the expression

P = 2(5x + 3x + 4)

P = 2(8x + 4)

Now expand the bracket

P = 2 x 8x + 2 x 4

P = 16x + 8

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the sum of the internal angles of a triangle are equal to 180 degrees.

once i remembered that the problem became a lot easier.

let a, b, and c be the angles of the triangle.

-----

let a = 2*b

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let c = a+b-12

-----

the above two statements are given.

since the sum of the internal angles of a triangle are equal to 180, then we have a third equation to work with which is

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a + b + c = 180

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we now have 3 equations for 3 unknowns and we should be able to solve for each of the unknowns.

-----

it looks like the easiest thing is to solve for b. once we find b, the rest should fall into place very nicely.

-----

since a = 2*b, we can substitute 2*b for a in the equation a + b + c = 180.

that equation then becomes 2*b + b + c = 180 which becomes 3*b + c = 180.

looking at the equation c = a + b - 12, we solve for b as follows:

since we know that a = 2 * b, we can substitute 2*b for a and the equation becomes c = 2*b + b - 12 which becomes c = 3*b - 12.

-----

the equation we are working with is 3*b + c = 180 which originally started as a + b + c = 180.

we can substitute 3*b - 12 for c and the equation becomes

3*b + 3*b - 12 = 180 which becomes 6*b = 192 after adding 12 to both sides and combining like terms.

dividing both sides of the equation by 6 and we get b = 32 degrees.

-----

we have b = 32 degrees.

we have a = 2 * b so a = 64 degrees.

we have c = a + b - 12 which becomes c = 32 + 64 - 12 which becomes c = 96 - 12 which becomes c = 84 degrees.

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substituting in the equation a + b + c = 180, we get 32 + 64 + 84 = 180 which becomes 96 + 84 = 180 which becomes 180 = 180.

-----

answer is:

a

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