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Sagot :
Given:
Perimeter of rectangle = 220 inches
Ratio of length to width = 7:3
Use the perimeter of a rectangle formula:
P = 2(L + W)
220 = 2(L + W)
Divide both sides by 2:
[tex]\begin{gathered} \frac{220}{2}=\frac{2(L+W)}{2} \\ \\ 110=L+W \\ \\ \text{Subtract W from both sides:} \\ 110-W=L+W-W \\ \\ 110-W=L \end{gathered}[/tex]Take the ratio:
7W : 3L
7W = 3L
Divide both sides by 3:
[tex]\frac{7}{3}W=L[/tex]Substitute 7/3 W for L in (110 -W = L)
[tex]\begin{gathered} 110-W=\frac{7}{3}W \\ \\ \end{gathered}[/tex]Multiply through by 3:
[tex]\begin{gathered} 330-3W=7W \\ \\ 330=7W\text{ + 3W} \\ \\ 330=10W \\ \\ \frac{330}{10}=W \\ \\ 33=W \end{gathered}[/tex]To find L, we have:
110 - W = L
110 - 33 = L
77 = L
To find the Area, use the formula:
Area = Length x Width
Area = 77 x 33 = 2541 square inches
ANSWER:
2541 square inches
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