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The perimeter of a rectangle is 220 inches. The ratio of its length to its width is 7:3 Find the area of the rectangle

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