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A rectangular exercise has a perimeter of 36 week the length of the mat is twice the width it right and solve and equation to determine the length of the feet of the mat then find the area in square feet of the mat

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calculista

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]

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