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.

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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.

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calculista calculista · Answer 1 · 2025-03-21T21:13:52-04:00

Answer:

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

Part b) The area of rectangle 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]