Question

The area of the small shape is 35 square feet. The big shape is larger by a scale factor of 4/3. Find the area of the large shape to the nearest tenth.
a) 62.2 square feet
b) 140 square feet
c) 46.7 square feet
d) 186.7 square feet
e) none of these

Answer 1

Answer:

Option a) 62.2 square feet  

Step-by-step explanation:

we know that

The dilation is a non-rigid transformation that produces similar figures

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ----> the scale factor

x ----> the area of the large shape

y ----> the area of the small shape

so

$z^{2}=\frac{x}{y}$

we have

$z=\frac{4}{3}$

$y=35\ ft^2$

substitute

$(\frac{4}{3})^{2}=\frac{x}{35}$

$\frac{16}{9}=\frac{x}{35}$

solve for x

$x=\frac{16}{9}(35)=62.2\ ft^2$