Pergunta
The length of a rectangle multiplied by 3 is equal to 4 times its width. The perimeter is 8(2)/(5) feet. Find the length and the width.
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Renata MariaMestre · Tutor por 5 anos
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To solve this problem, we need to find the length and width of the rectangle.<br /><br />Given information:<br />- The length of the rectangle multiplied by 3 is equal to 4 times its width.<br />- The perimeter of the rectangle is $8\frac {2}{5}$ feet.<br /><br />Let's denote the length of the rectangle as "L" and the width as "1: Set up the equation for the relationship between the length and width.<br />L × 3 = 4W<br /><br />Step 2: Set up the equation for the perimeter of the rectangle.<br />Perimeter = 2(L + W)<br />$8\frac {2}{5}$ = 2(L + W)<br /><br />Step 3: Solve the system of equations.<br />From the first equation, we can express L in terms of W:<br />L = (4W) / 3<br /><br />Substituting this expression for L into the perimeter equation:<br />$8\frac {2}{5}$ = 2((4W) / 3 + W)<br />$8\frac {2}{5}$ = 2(7W / \frac {2}{5}$ = 14W / 3<br />W = $8\frac {2}{5 3 / 14<br />W = 1.4 feet<br /><br />Step 4: Find the length using the expression for L in terms of W.<br />L = (4W) / 3<br />L = (4 × 1.4) / 3<br />L = 1.867 feet<br /><br />Therefore, the length of the rectangle is approximately 1.867 feet, and the width is 1.4 feet.
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