In a rectangle, the perimeter is 102 inches. The width of the rectangle is 9 inch more than half the length. What are the length and width of the rectangle?show the legend (formula) Write the equation and solve it step by step. Write a sentence answering the question.
Accepted Solution
A:
ANSWERw=23 inches and l=28 inches.EXPLANATIONThe given rectangle has perimeter,[tex]p = 102in.[/tex]The width of the rectangle is 9cm more than half the length.[tex]w = \frac{1}{2} l + 9[/tex]Let the length be [tex]l[/tex]inches.The formula for perimeter is,[tex]p = 2l + 2w[/tex]We substitute the values to get,[tex]102 = 2l + 2( \frac{1}{2}l + 9)[/tex]Expand:[tex]102 = 2l + l + 18[/tex][tex]102 - 18 = 3l[/tex][tex]84 = 3l[/tex][tex]l = 28in.[/tex]The width is [tex]w = \frac{1}{2} (28) + 9[/tex][tex]w = 14 + 9 = 23in.[/tex]