A rectangle has a length 10 m less than twice its width. When 2 m are added to the width, the resulting figure is a sqaure with an area of 196 m squared. Find the demensions of the original rectangle
Width = X meters.
Length = (2X - 10) meters.
X + 2 = 2X - 10,
X = 12.
2X - 10 = 24 - 10 = 14.
10
Let's start by assigning variables to the dimensions of the rectangle. Let's call the width of the rectangle "w" (in meters) and the length "l" (in meters).
According to the given information, the length of the rectangle is 10 meters less than twice its width. So we can write the equation:
l = 2w - 10
Now, when 2 meters are added to the width, the resulting figure is a square with an area of 196 square meters. Since the figure is a square, the width and length will be the same. So we can write the equation:
(w + 2) * (w + 2) = 196
Expanding and simplifying this equation:
w^2 + 4w + 4 = 196
Now, let's solve this equation for the width "w":
w^2 + 4w + 4 - 196 = 0
w^2 + 4w - 192 = 0
Now we need to factorize this quadratic equation:
(w - 12)(w + 16) = 0
So, w - 12 = 0 or w + 16 = 0
If we solve for "w" in each case, we get:
w = 12 or w = -16
Since a negative width doesn't make sense in this context, we ignore w = -16.
Therefore, the width of the original rectangle is 12 meters.
Now, we can substitute this value back into the equation for the length of the rectangle:
l = 2w - 10
l = 2 * 12 - 10
l = 24 - 10
l = 14
So, the dimensions of the original rectangle are a width of 12 meters and a length of 14 meters.
To find the dimensions of the original rectangle, we can follow these steps:
1. Let's assume the width of the original rectangle is "w" meters.
2. According to the given information, the length of the original rectangle is 10 m less than twice its width. So the length can be expressed as (2w - 10) meters.
3. When 2 m are added to the width, the resulting figure is a square with an area of 196 m². Therefore, the new width is (w + 2) meters.
4. Since the resulting figure is a square, the new length will be equal to the new width. So, the new length is also (w + 2) meters.
5. The area of a square is calculated by multiplying its width by its length. According to the problem, the area of the resulting square is 196 m². Therefore, we can set up the equation: (w + 2) * (w + 2) = 196.
Now, we can solve this equation to find the value of w, which will give us the width of the original rectangle.