Example Question - rectangle perimeter
Here are examples of questions we've helped users solve.
Finding the Measurement of a Curtain in a Rectangular Dormitory
<p>Sea \( l \) la longitud del lado menor del dormitorio de Pablo y \( 8 \) la longitud del lado mayor. Entonces, el perímetro \( P \) se calcula como \( P = 2l + 2 \cdot 8 \).</p> <p>Sabemos que el perímetro total es de \( 28 \) metros, entonces establecemos la ecuación:</p> <p>\[ 28 = 2l + 2 \cdot 8 \]</p> <p>\[ 28 = 2l + 16 \]</p> <p>\[ 2l = 28 - 16 \]</p> <p>\[ 2l = 12 \]</p> <p>\[ l = 6 \]</p> <p>La cortina que divide el dormitorio en dos partes triangulares iguales será igual a la longitud de la diagonal del rectángulo formado por los lados \( l \) y \( 8 \) metros.</p> <p>Aplicando el teorema de Pitágoras para encontrar la longitud de la diagonal \( d \), tenemos:</p> <p>\[ d = \sqrt{l^2 + 8^2} \]</p> <p>\[ d = \sqrt{6^2 + 8^2} \]</p> <p>\[ d = \sqrt{36 + 64} \]</p> <p>\[ d = \sqrt{100} \]</p> <p>\[ d = 10 \]</p> <p>Por lo tanto, la cortina deberá medir \( 10 \) metros.</p>
Solving for Area and Perimeter of a Rectangle with Variables
The image you've provided shows a rectangle with its sides labeled in terms of x and y: The longer side (length) is labeled as "4x - y" and "x + 6y". The shorter side (width) is labeled as "3x + 1". To calculate the area of the rectangle, we multiply the length by the width. However, we first need to make sure both expressions for the length are equal. Let's set them equal to each other and solve for one of the variables: 4x - y = x + 6y 4x - x = 6y + y 3x = 7y x = 7y / 3 Now we have a relationship between x and y. To find the area, we could substitute x into one of the sides and then calculate the area. But since we do not have specific values for x and y, we cannot calculate a numeric value for the area without more information. For the perimeter, you add up all the sides: Perimeter (P) = 2(length) + 2(width) P = 2(4x - y) + 2(3x + 1) P = 8x - 2y + 6x + 2 P = 14x - 2y + 2 You can then replace x with (7y / 3) in the perimeter equation to express the entire perimeter in terms of y: P = 14(7y / 3) - 2y + 2 To simplify this: P = (98/3)y - 2y + 2 P = (98y - 6y) / 3 + 2 P = (92y / 3) + 2 Thus, we've simplified the perimeter equation, but without specific numeric values for x and y, we can't find an exact numerical value for the perimeter. It's worth noting that there might be a bit of confusion because the rectangle is labeled with two expressions for its length that seem to be equal without having additional information about the relationship between x and y besides the equation we've derived. Normally, you would need either a specific value or an additional equation to solve for x and y and hence calculate the area and perimeter with numeric values.
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