Question

3. The perimeter of a square S, is 12 m more than the
perimeter of the square S2. If the area of S, equals
three times the area of S, minus 11, then what is the
perimeter of S1?

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Answer 1

Answer:

32m is the perimeter of the square S1

Step-by-step explanation:

Let the side of the square S1 be "a"

Let the side of the square S2 be "b"

So, According to question

S1=S2+12

4a=4b+12(Perimeter of S1=4a, Perimeter of S2=4b)

Dividing the equation by 4, we get:-

a=b+3---------------(1)

and,

S1=3S2-11

(a)^2=3[(b)^2]-11 ----------------(2)

Putting the value of a in equation 2, we get:-

(b+3)^2=3(b)^2-11

b^2+9+6b=3(b)^2-11

6b+9=2(b)^2-11

6b+20=2(b)^2

2(b)^2-6b-20=0 ----------------(3)

Dividing the equation 3 by 2,we get:-

b^2-3b-10=0

b^2-5b+2b-10=0

b(b-5)+2(b-5)=0

(b-5)(b+2)=0

b=5,-2

Sides cannot be negative so b=5

a=b+3

a=5+3

a=8

Perimeter of S1=4×a

=4×8

=32m