Question

David currently has a square garden. He wants to redesign his garden and make

it into a rectangle with a length that is 3 feet shorter than twice its width. He
decides that the perimeter should be 60 feet.

Determine the dimensions, in feet, of his new garden.

Answer 1

Hence new dimension of new garden is 27 by 51

Explanation:

Initial dimension of his square garden = X by X

Final dimension of his rectangular garden = L by B

Perimeter of his garden = 60 = 4X

Hence X = 60/4 = 15 ft

Area of the square garden = 15 x 15 = 225 ft²

New garden dimensions

L + 3 = 2W-----------------Eqn 1

2(L+W) = 60---------------Eqn 2 (since both shapes have the same perimeter)

solving both equations simultaneously

From equation one L = 2W-3, it's now substituted into equation 2

from equation 2, 2L+2W= 60

Hence 2(2W-3) + 2W = 60

W = 27 ft

L= 2(27)-3= 51 ft

Hence length and breadth of new garden is 27 by 51

Answer 2

Width=11 feet

Length = 19 feet

Explanation:

Hi, to answer this question we have to write a system of equations :

• 2 L +2 W =60 (perimeter of a rectangle equals to 60)
• L =2W-3 (length that is 3 feet shorter than twice its width)

Where:

L= length

W= width

Replacing the value of L in the perimeter equation:

2(2W-3) +2W =60

4W -6+2W=60

4W+2W=60+6

6W=66

W=66/6

W=11

Replacing the value of W in the length equation:

L= 2(11)-3

L=22-3

L=19