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Vitek1552 [10]
3 years ago
14

Tomas drew a rectangular with an area of 6 square centimeters. What is the greatest possible perimeter for this rectangle

Mathematics
1 answer:
anzhelika [568]3 years ago
8 0
There is no "greatest" possible perimeter.

There's a smallest possible perimeter.  That's a square.
Since the area is 6 square centimeters, each side of the square is
√6 = about 2.45 cm, and the perimeter is about  9.8 cm (rounded).

But there's no 'greatest' perimeter.  You can take that square
and if you're careful, you can make it into rectangles that all have
the same area ... 6 square cm ... but the longer and skinnier
you make it, the greater the perimeter will be. 
You can give me a number as big as you want, and I can make
a rectangle with a perimeter of your number, but an area of only
6 square centimeters !

Here are some few examples.  They all have
the same area, but different perimeters:

2.45 cm by 2.45 cm ...   Area = 6 square cm ... Perimeter = 9.8 cm

2 cm by 3 cm ...              Area = 6 square cm ... Perimeter = 10 cm
1.5 cm by 4 cm ...           Area = 6 square cm ... Perimeter = 11 cm
1.2 cm by 5 cm ...           Area = 6 square cm ... Perimeter = 12.4 cm
1 cm by 6 cm ...              Area = 6 square cm ... Perimeter = 14 cm
0.8 cm by 7.5 cm ...        Area = 6 square cm ... Perimeter = 16.6 cm
0.6 cm by 10 cm ...         Area = 6 square cm ... Perimeter = 21.2 cm
0.5 cm by 12 cm ...         Area = 6 square cm ... Perimeter = 25 cm
0.4 cm by 15 cm ...         Area = 6 square cm ... Perimeter = 30.8 cm
0.3 cm by 20 cm ...         Area = 6 square cm ... Perimeter = 40.6 cm
0.2 cm by 30 cm ...         Area = 6 square cm ... Perimeter = 60.4 cm
0.1 cm by 60 cm ...         Area = 6 square cm ... Perimeter = 120.2 cm

0.001cm by 6,000cm ... Area = 6 square cm ... Perimeter = 12,000.2 cm
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The expressions D, E, and F represent a correct solution to the equation.

Step-by-step explanation:

Step 1:

First, we need to solve the given equation and find the value of x which satisfies the equation.

6(x+4)=20, (x+4) = \frac{20}{6}   = 3.333,

x = 3.333 - 4 = -0.666.

So the value of x for the given equation is -0.666.

Step 2:

Now we evaluate the values of the six given options to see which ones have an x value of -0.666.

A. \frac{20-4}{6}= \frac{16}{6}  = 2.666,

B. \frac{1}{6} (20-4)= \frac{1}{6} (16)=\frac{16}{6} = 2.666,

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E. \frac{1}{6} (20-24) = \frac{1}{6} (-4)= -0.666,

F. (20-24)\frac{1}{6} = (-4)\frac{1}{6} = -0.666.

So the options D, E, and F represent a correct solution to the given equation.

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