A rectangle has a length of (3.2a 1 0.18b) centimeters. The width is half the length. Sasha writes the expression (12.8a 1 0.72b) to represent the perimeter of the rectangle in centimeters. Is Sasha’s reasoning correct? Explain.

Perimeter of the rectangle will be given by:
P=2(L+W)
L=(3.2a 10.18b)
W=1/2(3.2a 10.18b)=(1.6a 5.9b)
Thus the perimeter will be:
P=2(3.2a 10.18b+1.6a 5.9b)
P=2(4.8a 16.08b)
P=(9.6a+ 32.16b)

Sasha was not correct

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parmesanchilliwack parmesanchilliwack · Answer 2 · 2019-04-25T08:14:22+02:00

Answer:

No, her reasoning is incorrect.

Step-by-step explanation:

Given,

The length of the rectangle,

[tex]l = ( 3.2a + 0.18b ) \text{ cm}[/tex],

Here, the width is half the length.

⇒ Width of the rectangle,

[tex]w = \frac{l}{2}=\frac{1}{2}(3.2a + 0.18b)=\frac{3.2a}{2}+\frac{0.18b}{2} = (1.6a + 0.09b)\text{ cm}[/tex]

We know that,

The perimeter of a rectangle is,

[tex]P=2(l+w)[/tex]

[tex]=2(3.2a + 0.18b+1.6a + 0.09b)[/tex]

[tex]=2(4.8a+0.27b)[/tex]

[tex]=(9.6a+0.54b)\text{ cm}[/tex]

Since, 9.6a + 0.54b ≠ 12.8a + 0.72b

Hence, her reasoning is incorrect.