Question

A rectangular garden is surrounded on its outside by 2m board path. If area of the path is 464square metre then what is the perimeter of the garden

Answer 1

Answer:

Perimeter = 456 m

Step-by-step explanation:

Define L and B

Let L be the length of the garden.

Let B be the breadth of the garden.

Form equation:

Area of the border = (L + 2 + 2) x 2 + (B x 2)

Area of the border = (L + 4) x 2 + (B x 2)

Area of the border = 2L + 8 + 2B

Solve L and B:

Given that the area of the path is 464 m²

464 = 2L + 8 + 2B

2L + 2B = 464 - 8

2L + 2B = 456 m

Find the perimeter:

Perimeter = 2L + 2B

Perimeter = 456 m

Answer: Perimeter = 456 m

Answer 2

Answer:

so perimeter = 216 m

Step-by-step explanation:

The width of the path is 2m

area of path is 464 m²

perimeter of garden=?

Now let x be the length of garden and y be the width of garden

perimeter of garden will be

2(x+y)

Now we know area of path = 464 square meter

and also area = length * width of path

Length of path = x+2+2 m

width of path = y + 2+2 m

area = (x+4)(y+4)

putting the value gives

464 = (x+4)(y+4)

464 = xy + 4x + 4y + 16

464-16 = xy + 4(x+y)

448 = xy + 4(x+y)

2(2(x+y))=448-xy

2(2(x+y))= (448)-(16)

2(x+y)= $\frac{432}{2}$

2(x+y)= 216 m

which is the perimeter of the garden

so perimeter = 216 m