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A rectangular exercise mat has a perimeter of 36 feet. The length of the mat is twice the width. Write and solve an equation to determine the length, in feet, of the mat. Then find the area, in square feet, of the mat.

Respuesta :

calculista

Answer:

Part a) The length of the mat is [tex]12\ ft[/tex]

Part b) The area of the mat is [tex]72\ ft^{2}[/tex]

Step-by-step explanation:

step 1

Find the length

Let

L-----> the length of the rectangle

W---> the width of the rectangle

we know that

The perimeter of rectangle is

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

[tex]P=36\ ft[/tex]

so

[tex]36=2(L+W)[/tex]

[tex]18=(L+W)[/tex] ----> equation A

[tex]L=2W[/tex] -----> equation B

substitute equation B in equation A

[tex]18=(2W+W)[/tex]

solve for W

[tex]18=3W[/tex]

[tex]W=18/3=6\ ft[/tex]

Find the value of L

[tex]L=2(6)=12\ ft[/tex]

step 2

Find the area

The area of rectangle is equal to

[tex]A=LW[/tex]

substitute the values

[tex]A=(12)(6)=72\ ft^{2}[/tex]

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