Question

A city planning committee is designing a rectangular community garden in one of the city’s parks. The perimeter of the garden will be 40 feet and the area will be 96 square feet. The length of one side of the garden is represented by x.

Write and solve an equation to determine, algebraically, the dimensions of the garden, in feet.

Answer 1

12ft by 8ft

Explanation:

Area of the rectangular park = Length × Breadth

Perimeter of the rectangular park = 2(L+B)

If the perimeter of the garden is 40 feet and the area is 96 square feet, the equations becomes;

A = LB

P =2(L+B)

96 = LB ...(1)

40 = 2(L+B)... (2)

From 1, L = 96/B

Substituting L = 96/B into 2 we have:

40 = 2(96/B+B)

20 = 96/B + B

20 = (96 + B²)/B

20B = 96+B²

B²-20B+96 = 0

(B² -12B)-(8B+96) = 0

B(B-12)-8(B-12) = 0

B-8 = 0 and B-12 = 0

B = 8 and 12

Substituting B =8 and 12 into equation 1

96 = LB

96 = 8L

L = 12

Thia means that the dimension of the rectangular garden is 12ft × 8ft