Answer to Question #312095 in Geometry for DenmRc

Question

ATOM is similar to IRON. The sides of ATOM are 3, 6, 9, and 12 centimeters. The shortest side of IRON is 2 centimeters long.​

a. What is the scale factor of ATOM to

IRON

b. Find the lengths of the two longest sides of IRON

c. Find the perimeter of IRON.

d. Find the ratio of the perimeters of ATOM and iRON.

Answer 1

$a) Scale factor = \frac{Dimension of the new shape}{Dimension of the original shape}$

$Dimension of new shape=2$

$Dimension of original shape=3$

Therefore;

$=\frac{2}{3}$

$=0.6667$

$b) Lengths of the two longest sides of IRON$

$i)9\times0.6667$

$=6centimeters$

$ii)12\times0.6667$

$=8centimeters$

$c) Perimeter of IRON$

The remaining lengths of IRON

shortest=2cm

$next=0.6667\times6$

$=4cm$

$next side=0.6667\times9$

$=6cm$

$Largest=0.6667\times12$

$=8cm$

So perimeter is the distance round the object

$=(2+4+6+8)centimeters$

$=20centimeters$

d) Ratio of the perimeters of ATOM and IRON

$Perimeter of IRON= 20centimeters$

$Perimeter of ATOM=(3+6+9+12)centimeters$

$=30centimeters$

Therefore;

Ratio of the perimeter of ATOM and IRON

$=Perimeter of ATOM:Perimeter of IRON$

$Ratio=30:20$

$=3:2$