"A rectangle has length 2x+4, and width x+3. If the area of this rectangle is 144m^2, calculate the perimeter.

(2x+4)(x+3)=144 ==> 2x^2+10x+12=144

2x^2+10x-132=0 ==> x^2+5x-66=0

Factoring results in

(x+11)(x-6) with x=-11,6

Since we can't have negative distances, x=6 and the length is 16 and the width is 9

Perimeter=50

Simple! For the perimeter, you need to add up all four sides. Two lengths of 4 1/2 yards, two widths of 3 yards: 4 1/2 + 4 1/2 + 3 + 3 = 15 For the area, use the formula for a rectangle, Area = Length x Height: 4 1/2 x 3 = 13 1/2

(2x + 4)(x + 3) = 144 ==> 2x^2 + 10x + 12 = 144

x^2 + 5x + 6 = 72 ===> x^2 + 5x - 66 = 0

(x + 11)(x - 6) = 0 ==>x = -11 or x = 6

x = 6

2x + 4 = 16

x + 3 = 9

Perimeter of rectangle = 2[(2x + 4) + ( x + 3)] = 2(3x + 7) =

2(18 + 7) = 2(25) = 50 meters

I am sorry but I am unable to sketch. I am sure that you can sketch the rectangle with the aforementioned dimensions.

The area is (2x+ 4)(x + 3)

= 2x^2 + 10x + 12, so

2x^2 + 10x + 12 = 144, so

2x^2 + 10x - 132 = 0, so

x^2 + 5x - 66 = 0, so

(x + 11)(x - 6) = 0, so

x = -11, or x = 6.

x = -11 is not possible, so x = 6,and

the length, 2x + 4 = 16,

the width, x + 3 = 9.

Check: 9 x 16 = 144.

The perimeter then is:

9 + 9 + 16 + 16 = 50.

Hope this helps, Twiggy.

LW = A

(2x + 4)(x + 3) = 144

2x^2 + 6x + 4x + 12 = 144

2x^2 + 10x - 132 = 0

x^2 + 5x - 66 = 0

(x - 6)(x + 11) = 0

x = 6, - 11 {discard negative root}

L = 2x + 4 = 12 + 4 = 16

W = x + 3 = 6 + 3 = 9

P = 2L + 2W = 32 + 18 = 50

check

16(9) = 144

A = (2x+4)(x+3) = 2x²+10x+12

144= 2x²+10x+12

0=x²+5x-66

0= (x+11)(x-6)

x=-11 (not possible)

x=6

length = 16

width = 9

Perimeter = 50

(2x + 4) (x + 3) = 144

2x² + 10x + 12 = 144

x² + 5x + 6 = 72

x² + 5x - 66 = 0

(x + 11) (x - 6) = 0

x = 6 is acceptable

L = 16 m

W = 9 m

P = 50 m