A=36 sq m p=30 m given the area and perimeter find length and width

Area (A) = 36 square metres

perimeter (P) = 30 metres

Formulae: 1) Area = length x width

2) perimeter = 2*(length+width)

let length be x meters and width be y meter

so A = x*y= 36

P=2(x+y)= 30

divide with 2 on both sides

2%28x%2By%29%2F2+=30%2F2

x+y =15eq(1)

rule : +%28x-y%29%5E2+=+%28x%2By%29%5E2-4xy

+%28x-y%29%5E2+=+%2815%29%5E2-4%2A36

+%28x-y%29%5E2+=+225-144

+%28x-y%29%5E2+=+81

apply square root on both sides

+sqrt%28x-y%29+=+sqrt%2881%29

x-y = 9 eq(2)

now we need to solve equation 1 &e to get x&y

add equation 1 & 2

x+y= 15

x-y =9

2x = 24

2x= 24

divide with 2 on both sides

+2x%2F2+=+24%2F2

x= 12

but x*y =36

12*y =36

divide with 12 on both sides

12y%2F12+=36%2F12

y= 3

so length (x)= 12 m

width (y) =3m

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step-by-step explanation: