Question

Please answer ASAP.

What are a) the ratios of the perimeters and b) the ratio of the areas of the larger figure to the smaller figure? The figures are not drawn to scale.

Answer 1

You will find the ratio of the perimeters by writing the length of 28 yards over 8 yards and simplifying it.

28/8 = 7/2

To find the ratio of the areas, you will multiply this by itself because there are two dimensions in an area.

7/2 x 7/2 = 49/4

The second choice is correct.

Answer 2

Answer with explanation:

→The Smaller Quadrilateral called image is a dilation of Larger Quadrilateral ,having dilation factor less than 1.

→So,when image has smaller size than preimage,it means

0< Dilation Factor <1

→Also,the Ratio of Corresponding sides,as well as area and perimeter of two Quadrilaterals will be congruent.

Dilation factor

`=(8)/(28)\\\\=(2)/(7)`

If 28,x,y and z are length of corresponding sides of larger Quadrilateral,that is pre image then 8,
`(2x)/(7),(2y)/(7),(2z)/(7)` are respectively corresponding side lengths of Image that is Smaller Quadrilateral.

→→Ratio of the perimeter of pre image and Image

`=(28+x+y+z)/(8+(2x)/(7)+(2y)/(7)+(2z)/(7))\\\\=(7*(28+x+y+z))/(2*(28+x+y+z))\\\\=(7)/(2)`

→→Ratio of areas of two Quadrilateral ,that is pre image and Image

=Square of Corresponding Side

`=(28^2)/(8^2)\\\\=(784)/(64)\\\\=(49)/(4)`

Option B