what is the equation?

Question

if three small squares are place side by side in a row, the result is a rectangle whose area in sq m is six times its perimeter in m. find a side of one of the squares

Answer 1

let x be the side of a square. Area of rectangle is
3m^2 which is 6(2(3m+m))
3m^2=48m
m^2=16m
m=16

Checking:
area is 3(16)(16)=768
perimeter is 2(3(16)+16))=8(16)128
6(128)=768 OK

Answer 2

Let one side be x. The area of one square is x^2. The area of the rectangle is 3x^2
The perimeter of the rectangle is 8x
So , you can write 3x^2 = 48 x and 3x = 48 x=16

the perimeter of the rectangle is 128

the area is 768 m^2

Answer 3

This means that the rectangle formed will have a length three times its width.
If width is w meters, the length is 3w.
Thus area A= (3* w^2)
Perimeter P= w+3w+w+3w=8w
As area in sq m is six times the perimeter in m, we have,
3w^2 = 6* 8w =48w
or
w^2 =16w
or
w = 16
Verification
Area = 3*(16*16) = 768
Perimeter = 16 +48+16+48 =128
We find Area = six times perimeter.

Answer 4

There are your equations.

A(r)=3s^2
A(r)=6P(r)
P(r)=2(3s+s)=8s

Solve for s.

Just to make this feel more complete, I'll go ahead and find the length of the side of one of the squares.

3s^2=6P(r)
s^2=2P(r)
s^2=16s
s=16

Checking my answer, the area is 16*48 or 768 sq m, while the perimeter is 2(48+16), or 128 m. 128*6=768, so 16 is indeed the answer.

Answer 5

let the length of the sq be x

3x * x = 6 * (x + x + 3x + 3x)
x = 16

Answer 6

3x^2 = 6(8x)
3x^2=48X
x^2 = 16
x = 4