Wire Cutting Problem - Finding the Length of a Square

[Peter G.]

Hi,

A strand of wire of length 32 cm is cut into two pieces One piece is bent to form a rectangle of width x cm and length (x+2) cm and the other piece is bent to form a square:

Show that the square has sides of length of (7-x) cm.

There are no answers in my book and I wanted to check whether what I did is right:

Length used in the total rectangle: 2x + 2(x+2) = 4x + 4

Square has 4 equal sides, hence, 4x:

4x + 4 + 4x = 32
4x = 28 - 4x
x = 7 - x

Thanks,
Peter G.

 

[eumyang]

Hi,

A strand of wire of length 32 cm is cut into two pieces One piece is bent to form a rectangle of width x cm and length (x+2) cm and the other piece is bent to form a square:

Show that the square has sides of length of (7-x) cm.

There are no answers in my book and I wanted to check whether what I did is right:

Length used in the total rectangle: 2x + 2(x+2) = 4x + 4

Square has 4 equal sides, hence, 4x:

I wouldn't use the 'x' variable again to denote the length of the side of the square, because 'x' is already used as the width of the rectangle and they are not the same. But otherwise, the work looks right.

4x + 4 + 4y = 32
4y = 28 - 4x
y = 7 - x

Thanks,
Peter G.

 

[Peter G.]

Ah, ok. Yeah, that's much better.

Thanks

 

[Peter G.]

Oh, if you don't mind, could you just help me out with this one too?

I have to complete the square for this: x² - 1/2x - 1/4 = 0 and give my answer as: a±b√n:

I got: 1/4 ± 1√5/16

but the book says: 1/4 ± √5/4

This is what I did to get to my answer:

x² - 1/2 x + 1/16 - 1/16 - 1/4 = 0
(x - 1/4)² - 1/4 - 1/16 = 0
(x - 1/4) = √5/16
x = 1/4 ±1√5/16

Thanks once again,
Peter G.

 

[HallsofIvy]

Oh, if you don't mind, could you just help me out with this one too?

I have to complete the square for this: x² - 1/2x - 1/4 = 0 and give my answer as: a±b√n:

I got: 1/4 ± 1√5/16

but the book says: 1/4 ± √5/4

This is what I did to get to my answer:

x² - 1/2 x + 1/16 - 1/16 - 1/4 = 0
(x - 1/4)² - 1/4 - 1/16 = 0
(x - 1/4) = √5/16
x = 1/4 ±1√5/16

Thanks once again,
Peter G.

When you took the square root of 5/16, you took the square root of the numerator but not of the denominator:
$$\sqrt{\frac{a}{b}}= \frac{\sqrt{a}}{\sqrt{b}}$$

 

[Peter G.]

Ah, ok, so the answer should really be, like in the book: √5/4, 4 being the √ 16. Got it, thanks.