The quadratic equation of the square is probably x2-5x+6.25 = 0 because its discriminant is equal to zero giving the equation equal roots of x = 5/2 and x = 5/2
Assign the rectangle a width 'x'. From the data in the problem the height is then '2x+1'. Multiplying the two together gives the area of the rectangle, which we know to be 45. In equation for this is: x(2x+1) = 45 or 2x^2 + x = 45. The roots of this equation can then be found either through the quadratic equation or a calculator solver (I used the solver because I'm lazy) and the answers are x = -5 and x= 4.5. The rectangle has a width of 4.5 and a height of 10.
Oh, what a happy little problem we have here! If the perimeter of the rectangle is 24 inches, we can use the formula P = 2l + 2w to find its dimensions. Since the length is 3 inches greater than the width, we can set up the equation 24 = 2(l + 3) + 2l and solve for l and w. With a little bit of math magic, we'll find that the dimensions of this lovely rectangle are 9 inches in length and 6 inches in width.
A rectangle by definition has two pairs of sides with equal length. Since perimeter equals the length of all the sides. The equation for the perimeter of a rectangle could be thought of as: 2L + 2W = P Where L represents the length of one side of the rectangle and W represents the length of the adjacent (next to) side of the rectangle. If you know the length of one side and the perimeter, plug those values in as L and P and then solve for W. That will give you L and W which are the dimensions of the rectangle.
Let the length be 2x+1 and the width be x: (2x+1)*x = 66 square yards 2x2+x = 66 2x2+x-66 = 0 Solving the above equation by means of the quadratic equation formula will give: x = -6 or x = 5.5, so x must be the latter because dimensions can't be negative. Therefore: length = 12 yards and width = 5.5 yards Check: 12*5.5 = 66 square yards
Let the length be 3x and the width be x: 3x*x = 243 3x2 = 243 Divide both sides by 3: x2 = 81 Square root both sides: x = 9 Therefore: length = 27 cm and width = 9 cm
x^2=3x(x-2)
4,3Improved Answer:-The dimensions work out as: 2.358898944 and 6.358898944 inches using the quadratic equation formula
To find the dimensions of a rectangle with an area of 100, you can use the formula for the area, which is length × width = area. Therefore, if one side is denoted as length ( l ) and the other as width ( w ), the equation becomes ( l \times w = 100 ). There are many possible pairs of dimensions that satisfy this equation, such as 10 and 10, 25 and 4, or 50 and 2. The dimensions can vary as long as their product equals 100.
Let the width of the rectangle be ( w ) cm. Then, the length can be expressed as ( w + 7 ) cm. The area of the rectangle is given by the equation ( w(w + 7) = 60 ). Solving this quadratic equation, we find that the dimensions of the rectangle are a width of 3 cm and a length of 10 cm.
If that's for a rectangle, the larger of the two dimensions is usually called the "length", the other one, "width".
Assign the rectangle a width 'x'. From the data in the problem the height is then '2x+1'. Multiplying the two together gives the area of the rectangle, which we know to be 45. In equation for this is: x(2x+1) = 45 or 2x^2 + x = 45. The roots of this equation can then be found either through the quadratic equation or a calculator solver (I used the solver because I'm lazy) and the answers are x = -5 and x= 4.5. The rectangle has a width of 4.5 and a height of 10.
the formula for the perimeter of a rectangle is p = 2W + 2L, where L is the length and W is the width, so your first equation is 126 = 2W + 2L"twice as long as it is wide" means that the length L is 2 times the width W, so your second equation is L = 2WIn order to solve for the dimensions, you can substitute L for 2W in the first equation to get:126 = L + 2L126 = 3LL = 126/3L = 42and because L = 2W:42 = 2WW = 42/2W = 21
Anything. No area is specified, so the dimensions are w*(4w+5) This equation lacks any value to define w.
Oh, what a happy little problem we have here! If the perimeter of the rectangle is 24 inches, we can use the formula P = 2l + 2w to find its dimensions. Since the length is 3 inches greater than the width, we can set up the equation 24 = 2(l + 3) + 2l and solve for l and w. With a little bit of math magic, we'll find that the dimensions of this lovely rectangle are 9 inches in length and 6 inches in width.
A rectangle by definition has two pairs of sides with equal length. Since perimeter equals the length of all the sides. The equation for the perimeter of a rectangle could be thought of as: 2L + 2W = P Where L represents the length of one side of the rectangle and W represents the length of the adjacent (next to) side of the rectangle. If you know the length of one side and the perimeter, plug those values in as L and P and then solve for W. That will give you L and W which are the dimensions of the rectangle.
area of the rectangle..
The base equation for calculating the area of a rectangle is length multiplied by width.