Question

Hw 28 shades figure

Answer 1

Prat 9)
`SF=2, x=16\ in`

Part 10)
`SF=0.5, x=14\ ft`

Part 11)
`SF=0.5, x=3.5\ ft`

Part 12)
`SF=3, x=7\ m`

Explanation:

we know that

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

Let

SF-----> the scale factor

a----> area of the shaded figure

b----> area of the unshaded figure

`SF^(2) =(x)/(y)`

Problem 9) we have

`a=216\ in^(2)`

`b=54\ in^(2)`

substitute in the formula

`SF^(2)=(216)/(54)`

`SF^(2)=4`

`SF=2` ------> the scale factor

To find the value of x, multiply the length of the unshaded figure by the scale factor

`x=(2)(8)=16\ in`

Problem 10) we have

`a=161\ ft^(2)`

`b=644\ ft^(2)`

substitute in the formula

`SF^(2)=(161)/(644)`

`SF^(2)=0.25`

`SF=0.5` ------> the scale factor

To find the value of x, multiply the length of the unshaded figure by the scale factor

`x=(0.5)(28)=14\ ft`

Problem 11) we have

`a=10.5\ ft^(2)`

`b=42\ ft^(2)`

substitute in the formula

`SF^(2)=(10.5)/(42)`

`SF^(2)=0.25`

`SF=0.5` ------> the scale factor

To find the value of x, multiply the length of the unshaded figure by the scale factor

`x=(0.5)(7)=3.5\ ft`

Problem 12) we have

`a=4,590\ m^(2)`

`b=510\ m^(2)`

substitute in the formula

`SF^(2)=(4,590)/(510)`

`SF^(2)=9`

`SF=3` ------> the scale factor

To find the value of x, divide the length of the shaded figure by the scale factor

`x=(21)/(3)=7\ m`