What is the length and width of a 864 square feet
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Equation for Perimeter of a rectangle: Perimeter = 2W + 2L
<h3>Defining the variables, let</h3>
<h3>Width = x</h3><h3>Length = 2x+3 (3 more than twice the width)</h3>
<h3>Plugging everything into the equation</h3>
<h3>30= 2(x) + 2(2x+3) using the distributive property,</h3><h3>30=2x+4x+6 combining like terms</h3><h3>30=6x+6 subtracting 6 from both sides,</h3><h3>24=6x divide both sides by 6</h3><h3>4=x This means that the width is 4 m.</h3><h3>To get the length, use the expression L=2x+3 and plug in x = 4 that was already solved for</h3><h3>L=2(4)+3</h3><h3>L=8+3 = 11 m</h3>
<h3>So the dimensions of the rectangle are width is 4 m and length is 11 m.</h3>
If your directrix is a "y=" line, that means that the parabola opens either upwards or downwards (as opposed to the left or the right). Because it is in the character of a parabola to "hug" the focus, our parabola opens upwards. The vertex of a parabola sits exactly halfway between the directrix and the focus. Since our directrix is at y = -2 and the focus is at (1, 6) AND the parabola opens upward, the vertex is going to sit on the main transversal, which is also the "line" the focus sits on. The focus is on the line x = 1, so the vertex will also have that x coordinate. Halfway between the y points of the directrix and the focus, -2 and 6, respectively, is the y value of 2. So the vertex sits at (1, 2). The formula for this type of parabola is where h and k are the coordinates of the vertex and p is the DISTANCE that the focus is from the vertex. Our focus is 4 units from the vertex, so p = 4. Filling in our h, k, and p:
. Simplifying a bit gives us
. We can begin to isolate the y by dividing both sides by 16 to get
. Then we can add 2 to both sides to get the final equation
, choice 4 from above.