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Tamara is creating a model of a rectangle. She has 26 inches of yellow ribbon to use for the border of the rectangle. She wants the length, l, to be 3 inches greater than the width, w. Which system of equations could Tamara use to find the dimensions of a rectangle that uses all of the ribbon?

Respuesta :

meerkat18
Let l and w be the length and width, respectively. Given that length is 3 inches greater than the width, it can be expressed as w + 3. Tamara has 26 inches of ribbon for the border which means that the perimeter of the rectangle should be 26. For rectangles, 
                                 P = 2L + 2W
Substituting the known values,
                                 26 = 2 (w + 3) + 2w
Simplifying, 
                                   26 = 4w + 6

Thus, w is 5 inches and length is 8 inches. 
calculista

Let

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

W------> the width of the rectangle

we know that

the perimeter of the rectangle is equal to

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

[tex]P=26\ in[/tex] -----> because Tamara's using the whole ribbon

so

[tex]26=2L+2W[/tex] -------> equation A

[tex]L=W+3[/tex] -------> equation B

Substitute equation B in equation A

[tex]26=2(W+3)+2W[/tex]

[tex]26=2W+6+2W[/tex]

[tex]4W=26-6[/tex]

[tex]W=5\ in[/tex]

find the value of L

[tex]L=W+3=5+3=8\ in[/tex]

therefore

the answer is

The system of equations is

[tex]26=2L+2W[/tex]

[tex]L=W+3[/tex]