Math HELP!!!? I need some help as soon as possible?

Question

If a 5 cm piece of wire is cut into two parts so that one part is four times as long as the other, what is the length of the longer part???

If a 5 cm piece of wire is cut into two parts such that a square formed by bending one part will have four times the area of a square formed by bending the other part, what is the length of the long part???

Answer 1

4cm

if you split up 5 cm into 5 parts

1cm    1cm    1cm    1cm    1cm  you have one and 4 times that

Answer 2

Good Problem!

Part I

let x = small piece

let 4x = larger piece

so that x+4x=5(cm) or 5x=5  therefore

x=1 (cm)                  small piece length

4x= 4 (cm)                 length of the long piece

Part II

Little tricky for me:

let Area1=x = s^2 formula for area1: side times side

let Area2=4x = (s1)^2  formula for area2: side1 times side1

Rem:      s is the small square side

and         s1 is the larger square side

Perimeter formula gives: 4*s for small square and 4*(s1) for the large square which must equal the original length of the wire: 5 cm. So we have

                                                 4*s + 4*s1 = 5

another equation to help solve the problem.

Now that we have three equations and three unknowns we can solve.

Since 4x= s1^2, we have x= (1/4) s1^2

therefore  a substitution from Area1gives:

s^2 = (1/4) s1^2  or s=sqrt[(1/4) s1^2]

                              s = (1/2)s1

                           or s1= 2s

Subing this in our Perimeter equation 4s+4(s1)=5 gives:

4s+4(2s)=5

4s+8s=5

12s=5

s=5/12

s1=10/12 = 5/6

Area1=s^2=25/144

and   Area2=s1^2=100/144 (can reduce)

done.

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