A square and a rectangle have the same perimeter. The length of the rectangle is 4cm less than twice the side of the square, and the width of the rectangle is 6 cm than the side of the square. find the perimeter of each figure
its actually 10...
To find the perimeter of each figure, let's first assign variables to represent the unknowns that we need to find.
Let's say the side length of the square is 's'.
According to the information given, the length of the rectangle is 4cm less than twice the side of the square, which means the length of the rectangle is (2s - 4) cm.
The width of the rectangle is 6 cm more than the side of the square, which means the width of the rectangle is (s + 6) cm.
The perimeter of a square is given by 4 times the side length. So, the perimeter of the square is 4s cm.
The perimeter of a rectangle is given by twice the sum of its length and width. So, the perimeter of the rectangle is 2*(length + width) cm.
Now, let's calculate the perimeter of each figure:
Perimeter of the square = 4s cm
Perimeter of the rectangle = 2*((2s - 4) + (s + 6)) cm
Simplifying the perimeter of the rectangle:
= 2*(3s + 2) cm
= 6s + 4 cm
Since the square and the rectangle have the same perimeter, we can equate the two expressions for their perimeters:
4s = 6s + 4
To solve for 's', let's bring the variables to one side and constants to the other side:
4s - 6s = 4
-2s = 4
s = 4 / -2
s = -2
However, a negative side length is not possible in this context. Therefore, there might be some mistake in the information provided. Please recheck the values or constraints given in the problem.
<<...the width of the rectangle is 6 cm than the side of the square>
6 cm more or 6 cm less
I am going to assume it is "less"
so we would have
(2x-4)(x-6) = x^2
Solve for x and take it from there
if it is "more" then
(2x-4)(x+6) = x^2 and solve
Check my thinking on this.
S = side of the square.
L= length of rectangle.
W = width of rectangle.
4S = perimeter of square
2L + 2W = perimeter of rectangle.
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perimeter is the same; therefore,
4S = 2L + 2W
2S = L + 4
S = W+6
Solve for S, L, W and calculate perimeter. I tried this and have S = 10, L = 16
W = 4
All of the units are cm.
Perimeter is 40 cm.
thank u
scrap my solution, I misread the question.
go with DrBob's method.