4 [ 4(x+3) ] = 16(x+3)
if you double the dimensions of any figure, you multiply the corresponding areas by 4
area ratio is proportional to length ratio squared for similar figures.
if you double the dimensions of any figure, you multiply the corresponding areas by 4
area ratio is proportional to length ratio squared for similar figures.
If the dimensions of the rectangle are doubled, the new length would be 2(x + 3) and the new width would be 2x. To find the area of the new rectangle, you multiply the new length by the new width:
Area of the new rectangle = New length × New width
= (2(x + 3)) × (2x)
= 4(x + 3)(x)
= 4x(x + 3)
So, the area of the new rectangle in terms of x is 4x(x + 3) square units.
Now, let's compare the ratio of the area of the original rectangle to the area of the new rectangle:
Ratio = Area of the original rectangle / Area of the new rectangle
= (4(x + 3)) / (4x(x + 3))
= (x + 3) / x
From the calculation, we can see that the ratio of the two areas is (x + 3) / x, which depends on the value of x. Therefore, the ratio will not be the same for any positive value of x.