solution to word problems through quadratic equation

Question

I want it to be answered urgently.'"A wire of length 200 cm is cut into two parts and each part is bent to form a square.If the area of the larger square is 9 times that of the smaller square,find the perimeter of the larger square."'.

Answer 1

let n=the side if the larger square

let x=the side of the smaller square

P=4n

P=4x

n^2=9*x^2

200=4n+4x

50=n+x

50-n=x

n^2=9(50-n)^2

n^2=9(2500-100n+n^2)

n^2=22,500-900n+9n^2

8n^2-900n+22,500=0

divide both sides by 4

2n^2-225n+5625=0

using the quadratic formula would be easier but I like to factor

2*5625=2*5*5*3*5*3*5=(2*5*5*3)*(5*3*5)=150*75 and 150+75=225

factor

(2n-75)(n-75)=0

n-75=0

n=75 will not work because you will use up the entire 200 cm on the larger square

2n-75=0

2n=75

n=37.5 cm

P=4*37.5

P=150 cm is the perimeter of the larger square  (answer)

300-150=150

150/4=12.5

check

the sides of the smaller square are each 12.5 cm

A=37.5^2=1406.25 sq cm

A=12.5^2=156.25

9*156.25=1406.25