The length of a rectangle is 2 meters more than its width. If the area is 35 square meters, what are the length and width? (Points : 4)
x times (x+2)=35 meters
x squared plus 2x = 35 meters
(x+7)(x+5)-35=0
x+7=0 x=7 meters the length
x+5=0 x=5 the width I believe this is correct But math is not my strongest subject. History and Geography are. :)
To find the length and width of the rectangle, we can use the given information that the length is 2 meters more than the width. We also know that the area of the rectangle is 35 square meters.
Let's start by assigning variables to the length and width. Let's say the width is 'w' meters. Since the length is 2 meters more than the width, the length would be 'w + 2' meters.
The formula for calculating the area of a rectangle is: Area = Length * Width. Using the given information, we can write the equation as:
35 = (w + 2) * w
Now, let's solve this equation to find the width. We can start by simplifying the equation:
35 = w^2 + 2w
Rearranging the equation to make it a quadratic equation:
w^2 + 2w - 35 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or using the quadratic formula.
Factoring: Unfortunately, this quadratic equation cannot be factored easily.
Completing the square: To complete the square, we need to convert the equation into a perfect square trinomial:
w^2 + 2w = 35
w^2 + 2w + 1 = 35 + 1 (Adding 1 to both sides to create a perfect square trinomial)
(w + 1)^2 = 36
Taking the square root on both sides:
w + 1 = ±√36
w + 1 = ±6
Solving for w:
Case 1: w + 1 = 6
w = 6 - 1 = 5
Case 2: w + 1 = -6
w = -6 - 1 = -7
Since the width of a rectangle cannot be negative, we discard the negative solution.
So, the width of the rectangle is 5 meters.
Now, we can calculate the length by substituting the value of the width back into the equation:
Length = Width + 2
Length = 5 + 2
Length = 7 meters
Therefore, the length of the rectangle is 7 meters and the width is 5 meters.