Jack wants to model a situation where the perimeter of the rectangle to the right is 6 feet plus or minus 1.5 feet. Because he is modeling a length "plus or minus" another length, he decides to use an absolute value equation for his model. Do you agree with his decision? Explain your reasoning.

Question

17-09-2022
Mathematics

Answered

Jack wants to model a situation where the perimeter of the rectangle to the right is 6 feet plus or minus 1.5 feet. Because he is modeling a length "plus or minus" another length, he decides to use an absolute value equation for his model. Do you agree with his decision? Explain your reasoning.

Answer :

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shivishivangi1679 shivishivangi1679 · Answer 1 · 2022-09-24T01:23:12-04:00

The absolute value of the equation will not work because the value of x would have to be negative for the perimeter to be 6 ft plus or minus 1.5 ft.

What is the perimeter of the rectangle?

The perimeter of the rectangle is given as:

Perimeter = 2(Length + Breadth)

The perimeter of a rectangle is 6 feet plus or minus 1.5 feet.

So, we have:

Perimeter = 2(Length + Breadth) = 6 feet ± 1.5 feet.

Then Substitute values for length and width

2(Length + Breadth) = 6 feet ± 1.5 feet.

2(4 + x) = 6 feet ± 1.5 feet.

Now,

2(4 + x) = 6 feet + 1.5 feet.

8 + 2x = 6.5 ft

2x = 6.5 - 8

x = -0.25 ft

2(4 + x) = 6 feet - 1.5 feet.

8 + 2x = 4.5 ft

2x = 4.5 - 8

x = -1.75ft

Here Both values of x are negative.

This means that the absolute value model can't work, because a rectangle cannot have a negative dimension.