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The perimeter of the triangle is 41 inches. The perimeter of the rectangle is 66 inches.
(Note: Pictures are not drawn to scale)
Part A: Write a system of equations to determine x and y.

Part B: Solve the system of equations. Use your solution to determine the length and width of the rectangle.

The perimeter of the triangle is 41 inches The perimeter of the rectangle is 66 inches Note Pictures are not drawn to scale Part A Write a system of equations t class=

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Answer:

Part A)  The system of equations is equal to

[tex]41=4x+7y[/tex]

[tex]33=(3x+7y)[/tex]

Part B)

The length is [tex]24\ in[/tex]

The width is [tex]9\ in[/tex]

Step-by-step explanation:

Part A)

we know that

The perimeter of the triangle is equal to the sum of the length of its three sides

In this problem

[tex]41=x+3x+7y[/tex]

[tex]41=4x+7y[/tex] -----> equation A

The perimeter of rectangle is equal to

[tex]P=2(L+W)[/tex]

In this problem

[tex]66=2(3x+7y)[/tex]

[tex]33=(3x+7y)[/tex] ------> equation B

Part B)

Using a graphing tool

Solve the system of equations

We know that

The intersection point both graphs is the solution of the system of equations

[tex]41=4x+7y[/tex]

[tex]33=(3x+7y)[/tex]

The intersection point is [tex](8,9/7)[/tex]

see the attached figure

[tex]x=8\ in[/tex]

[tex]y=(9/7)\ in[/tex]

step 3

Find the length and width of the rectangle

The length is 3x

[tex]3*8=24\ in[/tex]

The width is 7y

[tex]7*(9/7)=9\ in[/tex]

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PART A

Perimeter is the distance around the figure.

The perimeter of the triangle is 41 inches.

This implies that,

[tex]3x + x + 7y = 41[/tex]

[tex]4x + 7y = 41...(1)[/tex]

The perimeter of the rectangle is 66 inches.

This implies that,

[tex]2(7y + 3x) = 66[/tex]
Or

[tex]7y + 3x = 33...(2)[/tex]

PART B

The system of equations are

[tex]4x + 7y = 41...(1)[/tex]

[tex]7y + 3x = 33...(2)[/tex]

Subtract equation (2) from equation (1).

This gives us,

[tex]4x - 3x = 41 - 33[/tex]

[tex]x = 8[/tex]

Put this value into equation (2) to find y.

[tex]7y + 3(8) =33[/tex]

[tex]7y + 24 = 33[/tex]

[tex]7y = 33- 24[/tex]

[tex]7y =9[/tex]

[tex]y = \frac{9}{7} [/tex]

The length of the rectangle is

[tex]3(8)=24\:in[/tex]

The width of the rectangle is

[tex]7(\frac{9}{7})=9\: in[/tex]

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