Question

To fence a rectangular farm of 750 m², 110 m of fence has been used. Calculate the dimensions of the farm.

Answer 1

area lb=750
perimeter 2(l+b)=110
we know that
(l+b)^2=(l-b)^2+4lb
55^2=(l-b)^2+4*750
3025=(l-b)^2+3000
(l-b)^2=3025-3000
(l-b)^2=25
(l-b)=5
so,
solve equations
l+b=55 and l-b=5
l=30
substitute in any of the above equations u will get 
b=25
therefore the dimensions of the farm are 30m and 25m

Answer 2

The dimensions of the farm are 30m & 25m

Step-by-step explanation:

Given:

Area of the rectangular farm = 750m²

Fence used for the farm= 110m

To find:

the dimensions of the farm

Solution:

The area of the farm is 750sqm

Now, as we know,

Area of farm = L X B

∴ 750 = L X B.................(1)

The fence required is given

That is the perimeter of the farm is 110m

∴ The perimeter of the farm = 2(L+B)

∴ 110 = 2(L+B)

∴ 110/2 = (L+B)

∴ 55 = (L+B)

∴ 55 - L = B

∴ B = 55-L ........................(2)

Putting (2) in equation (1)

∴ 750 = L X B

∴ 750 = L X (55-L)

∴ 750 = 55L-L²

∴ 55L- L²= 750

∴  L²-55L + 750 = 0

Solving using quadratic equations

∴  L²-30L-25L+ 750 = 0

∴  L(L-30)- 25(L-30) = 0

∴  (L-30) (L-25) =0

∴  (L-30)= 0 or (L-25) =0

∴  L= 30 or  L= 25

When L = 30m the breadth (B) will be B = 55-30 = 25m

and when L= 25m the breadth (B) will be B = 55-25 =30m

Thus, the dimensions of the farm are 30m & 25m

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