a rectangle has an area of 4(x+3)square units. if the dimensions are doubled what is the area of the new rectangle terms of x.will the ratio of the area of the original rectangle to the area of the larger rectangle be the same for any positive value of x?
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.
To find the area of a rectangle, you multiply its length by its width. In this case, the area of the rectangle is given as 4(x + 3) square units.
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.