# What is a rectangle with a area of 36cm2 and a perimeter of 30cm

Area of  the Rectangle = 36 Cm2

Area of the Rectangle formula = Length × Width

Length × Width = 36 Cm2

Perimeter of the Rectangle = 30 Cm

Perimeter of the Rectangle formula  = 2(Length + Width)

2(Length + Width) = 30Cm

Divide each side by 2

Length + Width = 30/2

Length + Width =15

Width =15-Length

Length × Width = 36Cm2

Substitute Width in the above form.

Length (15 - Length) = 36Cm2

15 (Length) - (Length)2 = 36Cm2

Subtract each side 15 (Length)

- (Length)2 = -15 (Length) +  36Cm2

0 = (Length)2 -15 (Length)+ 36Cm2

(Length)2 - 15 (Length) + 36Cm2 = 0

(Length)2 -12(Length) - 3(Length) + 36= 0

Commom term Length and 3

Length ( Length -12 ) - 3 ( Length - 12) = 0

common term ( Length - 12 )

( Length - 12 ) ( Length - 3 ) = 0

Length -12 = 0 or Length - 3 = 0

Length =12 or Length = 3

Maximum value is Length

Length = 12

Width = 15 - Length

Width = 15 - 12

Width = 3

Length = 12 and Width = 3.

Rectangle area is given by A = l * w = 36 cm^2. where l is length and w is width.
Perimeter is given by P = 2(l+w) = 30 cm.
l + w = 15
l = 15-w
substitute l = 15-w in l * w = 36
(15-w) * w = 36
15w - w^2 = 36
w^2 -15w + 36 = 0
w^2 -12w -3w + 36 = 0
(w - 12) -3 (w - 12) = 0
w = 3 or w =12
l = 15 -w = 15 - 12 = 3
l = 15 -3 = 12
length = 12 cm and width = 3cm