The side of a rectangle are increased by a scale factor for the perimeter of the smaller rectangle is 20 cm what is the perimeter of the larger rectangle.please help eneone !!!!!!!
Since perimeter is directly proportional to the lengths of the sides of the rectangle,
it will have the same scale factor. Use this to determine your answer.
I find it hard to understand your gibberish sentence.
To find the perimeter of the larger rectangle, we first need to determine the scale factor by which the side lengths of the smaller rectangle were increased.
Let's assume the original length and width of the rectangle are L and W, respectively. Since the sides were increased by a scale factor, the new length and width of the rectangle become L + kL and W + kW, where k is the scale factor.
The perimeter of the smaller rectangle can be calculated using the formula:
Perimeter = 2(L + W)
Given that the perimeter of the smaller rectangle is 20 cm, we have:
20 = 2(L + W)
Now, let's substitute the new values for length and width into the equation:
20 = 2(L + kL + W + kW)
Simplifying the equation:
20 = 2L + 2kL + 2W + 2kW
Factoring out the common terms:
20 = 2(L + W) + 2k(L + W)
We can see that (L + W) appears in both terms on the right side of the equation. Let's define (L + W) as P: (L + W) = P.
20 = 2P + 2kP
Rearranging the equation:
20 = 2(1 + k)P
Dividing both sides by 2(1 + k):
10 = P(1 + k)
Simplifying further:
10/P = 1 + k
Now we can solve for k:
k = (10/P) - 1
Once you know the value of k, you can calculate the dimensions of the larger rectangle by multiplying the original dimensions by the scale factor:
New length = (1 + k) * original length
New width = (1 + k) * original width
Finally, to find the perimeter of the larger rectangle, use the formula:
Perimeter = 2(New length + New width)