Question

Hw 28 shades figure

Answer 1

Answer:

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) $SF=3, x=7\ m$

Step-by-step 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

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

Problem 9) we have

$a=216\ in^{2}$

$b=54\ in^{2}$

substitute in the formula

$SF^{2}=\frac{216}{54}$

$SF^{2}=4$

$SF=2$ ------> 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

$SF^{2}=\frac{161}{644}$

$SF^{2}=0.25$

$SF=0.5$ ------> 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

$SF^{2}=\frac{10.5}{42}$

$SF^{2}=0.25$

$SF=0.5$ ------> 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

$SF^{2}=\frac{4,590}{510}$

$SF^{2}=9$

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

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

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