A square in a rectangle have the same perimeter. The length of a side of the square is 4x-1. The length of the rectangle is 2x+2
1 answer:
The value x is 1, if the perimeter of square and rectangle are same. The perimeter of square and rectangle is 12 units.
Step-by-step explanation:
The given is,
A square in a rectangle have the same perimeter
The length of a side of the square is 4x-1
The length of the rectangle is 2x+2 and width is 2x
Step:1
Let, a - Side of square
l - Length of the rectangle
w - Width of the rectangle
Step:2
Formula for perimeter of square is,
.............................(1)
Formula for perimeter of rectangle is,
....................(2)
Step:3
From given,
Equation (1) = Equation (2)
where,
a = 4x-1
l = 2x+2
w = 2x
Substitute the values,
4 ( 4x-1 ) = 2 ( 2x+2+2x )
16x - 4 = 2 (4x + 2)
16x - 4 = 8x + 4
16x - 8x = 8
8x = 8
x = 1
Step:4
Substitute the values of x,
a = 4(1)-1 = 3
l = 2(1)+2) = 4
w = 2(1) = 2
Perimeter of square and rectangle is 12 units
Result:
The value x is 1, if the perimeter of square and rectangle are same. The perimeter of square and rectangle is 12 units.
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Answer: 271
Step-by-step explanation:
The formula we use to find the sample size is given by :-
, where is the two-tailed z-value for significance level of
p = prior estimation of the proportion
E = Margin of error.
If prior estimation of the proportion is unknown, then we take p= 0.5 , the formula becomes
Given : Margin of error : E= 0.05
Confidence level = 90%
Significance level
Using z-value table , Two-tailed z-value for significance level of
Then, the required sample size would be :
Simplify,
Hence, the required minimum sample size =271