One side of a rectangular piece of metal becomes double the other side, when the longer side is increase by 3x and the shorter side is increased by 2m. The area is also doubled. Find the dimensions of the given piece of metal
One side of a rectangular piece of metal becomes double the other side, when the longer side is increase by 3x and the shorter side is increased by 2m. The area is also doubled. Find the dimensions of the given piece of metal
Answer:
Length (L) = 3x
Step-by-step explanation:
Let's break down the problem step by step.
Let's assume the original dimensions of the rectangular piece of metal are:
Length = L
Width = W
According to the problem, when the longer side (length) is increased by 3 times (3x) and the shorter side (width) is increased by 2 meters (2m), the new dimensions become:
New length = L + 3x
New width = W + 2
We are also told that the new dimensions result in an area that is double the original area.
Step 1: Calculate the original area
Original area = Length × Width = L × W
Step 2: Calculate the new area
New area = New length × New width = (L + 3x) × (W + 2)
According to the problem, the new area is double the original area, so we can set up the equation:
2 × Original area = New area
Substituting the values, we have:
2 × (L × W) = (L + 3x) × (W + 2)
Step 3: Simplify the equation
Expand the equation:
2LW = LW + 2L + 3xW + 6x
Combine like terms:
LW - 2L - 3xW - 6x = 0
Now, let's rearrange the equation to group the variables together:
LW - 3xW - 2L - 6x = 0
Factoring out common terms:
W(L - 3x) - 2(L + 3x) = 0
At this point, we can see two terms multiplied by (L - 3x) and (L + 3x). We set each of these factors to zero:
L - 3x = 0
L + 3x = 0
Solving these equations individually, we get:
L = 3x
L = -3x
Since we are dealing with the dimensions of a physical object, negative values don't make sense in this context. Therefore, we can ignore the solution L = -3x.
Hence, the dimensions of the given piece of metal are:
Length (L) = 3x
Width (W) = Any value
Please note that the width can have any value as long as the length is three times the value of x.
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