Question

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

Answer 1

Area (A)=36 square meters
Perimeter (P)=30 meters
Formula: 1) Area=length x width
2) Perimeter=2x(length + width)
Let length be X meters and width be Y meters
So A=X x Y=36
P=2(X + Y)=30
Divide with 2 on both sides
2(X + Y)/2=30/2
X + Y=15
(X-Y)^2=(X+Y)^2-4XY
(X-Y)^2=(15)^2-4 x 36
(X-Y)^2=225-144
(X-Y)^2=81

Apply square root on both sides.
The square root of 81 is 9, so X-Y=9
Now we need to solve equation 1 to get X & Y, add equation 1 & 2.

X + Y=15
X - Y=9

2x=24
Now divide with 2 on both sides.

2x/2=24/2
X=12
But X x Y=36
12 x Y=36
Divide with 12 on both sides
12Y/12=36/12
Y=3
So length (X)=12 m
Width (Y)=3 m

Answer 2

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 =15................eq(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