PLEASE HELP ?
The length of a rectangle is 3 yd less than double the width, and the area of the rectangle is 65 yd2. Find the dimensions of the rectangle.
The length of a rectangle is 3 yd less than double the width means:
L = 2 W - 3
A = L ∙ W = ( 2 W - 3 ) ∙ W = 65
2 W ² - 3 W = 65
Subtract 65 to both sides
2 W ² - 3 W - 65 = 0
The solutions are:
W = 13 / 2 = 6.5
and
W = - 5
The width can't be so W = 6.5 yd
L = 2 W - 3 = 2 ∙ 6.5 - 3 = 13 - 3 = 10 yd
A = L ∙ W = 10 ∙ 6.5 = 65 yd ²
My typo.
The width can't be NEGTIVE so W = 6.5 yd
To find the dimensions of the rectangle, we need to set up an equation using the given information.
Let's say the width of the rectangle is "x" yards. According to the problem, the length of the rectangle is 3 yards less than double the width.
So the length = (2x - 3) yards.
The area of a rectangle is calculated by multiplying its length and width. In this case, the area is given as 65 square yards.
So, we can set up the equation:
Area = Length * Width
65 = (2x - 3) * x
To solve this equation, we can simplify it:
65 = 2x^2 - 3x
Rearranging the equation to standard form:
2x^2 - 3x - 65 = 0
Now, we can solve this quadratic equation for x using factoring, the quadratic formula, or graphing. Let's use factoring:
(2x + 13)(x - 5) = 0
Setting each factor equal to zero:
2x + 13 = 0 or x - 5 = 0
Solving for x:
2x = -13 or x = 5
x = -13/2 (We can ignore this negative value as length and width cannot be negative in this context)
x = 5
So, the width of the rectangle is 5 yards.
Now, we can find the length using the equation for the length we derived earlier:
Length = 2x - 3 = 2(5) - 3 = 10 - 3 = 7.
Therefore, the dimensions of the rectangle are:
Width = 5 yards
Length = 7 yards.