Question

The perimeter of a bigger square is 12 m
more than the perimeter of a smaller square.
Three times the area of the smaller square is
11 mº more than the area of the bigger square
Find the length of the bigger square.​

Answer 1

Step-by-step explanation:

Answer. let the length of side of smaller square be 'y' and the bigger be 'x'. 4x=12+4y, x=3+y, area of bigger square =x^2, area of smaller square=y^2, 3y^2=11+x^2, by substituting, 3y^2=11+(3+y)^2, y^2 -3y-10=0, "y=5" that is, length of the smaller one is5, x=5+3=8. therefore the length of the bigger square is 8.

Answer 2

Answer:

let the length of the bigger square is l m

area of the bigger square is l^2 sq m

perimeter of the bigger square is 4l m

perimeter of the smaller square (4l-12)m=4(l-3) m

so the length of the smaller square is( l-3) m

area of the smaller square is (l-3)^2 sq m

according to question,

3(l-3)^2-11=l^2

=> 3(l^2-6l+9) -11=l^2

=> 3l^2-18l+27-11-l^2=0

=> 2l^2-18l+16=0

=> 2(l^2-9l+8)=0

=> l^2-9l+8=0

=> l^2-8l-l+8=0

=> l(l-8)-1(l-8)=0

=> (l-8)(l-1)=0

=> l-8=0 => l=8

l-1=0 => l=1

so the length of the bigger square is 8 m

l is not equal to 1 m because then perimeter of the bigger square is 4 m and then perimeter of the smaller square is negative which is impossible.