Respuesta :
If the width of the rectangle is w and the length is l, then l=2w (since the rectangle is twice as long as it is wide) and w*l=w*(2w), as well as 2w+2l being 2w+2(2w)=2w+4w=6w. Since the perimeter (2w+2l) is the same as the perimeter of the square (if one side length of the square is x, then the perimeter is 4x), 6w=4x and by dividing both sides by 4, we get 6w/4=x=3w/2.
Since the area of the square is x^2, we can plug 3w/2 in for x to get
(3w/2)^2=9w^2/4 as the area of the square. Since the area of the square is 9 feet larger than the rectangle, 9w^2/4-9=2*l=w*(2w)=2w^2. Subtracting 2w^2 from both sides of 2w^2=9w^2/4-9 as well as adding 9 to both sides, we get w^2/4=9 and by multiplying 4 to both sides we get w^2=46 and by square rooting both sides we get w=sqrt(36)=6. Since the length is 2w, 6*2=12=the length. Since the area of the rectangle is l*w=6*12=72, the square's area is 9 more than that and is 72+9=81. Since x^2 is the area of the square which equals 81, 81=x^2 and by square rooting both sides we get x=9
Since the area of the square is x^2, we can plug 3w/2 in for x to get
(3w/2)^2=9w^2/4 as the area of the square. Since the area of the square is 9 feet larger than the rectangle, 9w^2/4-9=2*l=w*(2w)=2w^2. Subtracting 2w^2 from both sides of 2w^2=9w^2/4-9 as well as adding 9 to both sides, we get w^2/4=9 and by multiplying 4 to both sides we get w^2=46 and by square rooting both sides we get w=sqrt(36)=6. Since the length is 2w, 6*2=12=the length. Since the area of the rectangle is l*w=6*12=72, the square's area is 9 more than that and is 72+9=81. Since x^2 is the area of the square which equals 81, 81=x^2 and by square rooting both sides we get x=9
The dimension of rectangle : 6 and 12 units
square= 9 units
What is Perimeter ?
Perimeter is the distance around the edge of a shape.
Given:
let the width of rectangle be x.
length= 2x
let the side of square is y units.
Perimeter of rectangle = Perimeter of square
and, Area of square= Area of rectangle + 9
First, Perimeter of square= 4* side
= 4y units
Perimeter of rectangle,
=2(l+b)
=2(2x+x)
=6x units
Since, Perimeter of rectangle = Perimeter of square
6x=4y
3x=2y
Now, Area of square= Area of rectangle +9
y²= x*2x+9
y²= 2x²+9
y²= 2(2y/3)²+9
y²= 8y²/9+9
1/9 y²= 9
y²=81
y=±9
So, x=2y/3= 2*9/3
x= 6
Hence, dimension of rectangle is 6 and 12.
dimension of square is 9 units.
Learn more about perimeter here:
https://brainly.com/question/6465134
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