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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?

Verified Answer :

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

\(P=2L+2W\)

\(P=26\ in\) -----> because Tamara's using the whole ribbon

so

\(26=2L+2W\) -------> equation A

\(L=W+3\) -------> equation B

Substitute equation B in equation A

\(26=2(W+3)+2W\)

\(26=2W+6+2W\)

\(4W=26-6\)

\(W=5\ in\)

find the value of L

\(L=W+3=5+3=8\ in\)

therefore

the answer is

The system of equations is

\(26=2L+2W\)

\(L=W+3\)

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