A wire is first bent into the shape of a square. Each side of the square is 6cm long. Then the wire is unbent and reshaped into a rectangle. If the length of the rectangle is 9cm, what is its width?

Hi there!

Assuming a perfect square: we know there are 4 sides in a square, and all of them have equal length. This means that every side of the square is 6 cm, and with 4 sides, that would make an overall length / perimeter of 6 + 6 + 6 + 6, or 6*4, which would equal 24 cm. This means that our wire must be 24 cm long.

Now, for the rectangle. We know with rectangles that they also have 4 sides, and in pairs of 2 in terms of length (2 of the sides have the same length, and the other two have the same length). This means we know there are 2 sides that are 9 cm, which would mean 18 cm in total. This is the total amount of wire taken up by the length, but we are looking for the width. Thus, we can see how much wire is leftover not taken up by the length by subtracting 18 from 24:

24-18=6

Now, we see that the two sides that make up the width are 6 cm long. As those two sides are equal length, we can divide 6 cm into two equal parts to see the width.

6/2 = 3 cm.

Thus, the width of the rectangle is 3 cm.

Hope this helps!

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb