Comparing Perimeter and Area Compare the perimeter and area of the original figure to
the perimeter and area of the reduced figure using the
scale factor
Which statements are true about the comparison
between the two figures? Check all that apply.
The scale factor is 2.
The scale factor is
2.
6
The perimeter of the model is the product of the
scale factor and the perimeter of the original
rectangle
The area of the reduced figure is half the area of
the original figure
1
The area of the reduced figure is
times the
3
area of the original figure,
Intro
Done

- The scale factor is one-half

- The perimeter of the model is the product of the scale factor and the perimeter of the original rectangle

-The area of the reduced figure is (1/2)^2 = 1/4 times the area of the original figure

Step-by-step explanation:

The ratio of the length of the original rectangle to that of the reduced rectangle is 6 to 3, or a factor of 1/2. The ratio of the width of the original rectangle to that of the reduced rectangle is 2 to 1, or, again, a factor of 1/2. So, because this ratio of 1/2 is constant, we know the total scale factor is 1/2, making B correct.

The perimeter of a rectangle is: , where l is the length and w is the width. The perimeter of the reduced figure is: P = 2 * 3 + 2 * 1 = 6 + 2 = 8 units. The perimeter of the original figure is: P = 2 * 6 + 2 * 2 = 12 + 4 = 16 units.

Notice that 16 * (1/2) = 8, which means that the perimeter of the scale-factored, reduced rectangle is "the product of the scale factor (which is 1/2) and the perimeter of the original rectangle (which is 16)". So, C is correct.

The area of a rectangle is: , where l is the length and w is the width. The area of the reduced figure is: A = 3 * 1 = 3 units squared. The area of the original figure is: A = 6 * 2 = 12 units squared.

Notice that 12 * (1/4) = 3, which means that E is correct, but D is wrong.

Hope this helps!

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.