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julia-pushkina [17]
3 years ago
5

A farmer has a rectangular garden plot surrounded by 200 ft of fence. Find the length and width of the garden if its area is 247

5 ft2.
Mathematics
1 answer:
irina1246 [14]3 years ago
7 0

Answer:

l =45 --- length

w = 55 --- width

Step-by-step explanation:

Given

P  = 200 --- perimeter

A = 2475 --- area

Required

The dimension of the farm

Let

l \to length; w \to width

So:

p = 2(l+w) --- perimeter

2(l+w)=200

Divide by 2

l+w=100

Make l the subject

l = 100 - w

Also:

A= l*w --- area

l * w = 2475

Substitute: l = 100 - w

(100 - w) * w = 2475

Open bracket

100w - w^2 = 2475

Rewrite as:

w^2 - 100w +2475 = 0

w^2 - 45w - 55w +2475 = 0

Factorize

w(w - 45) - 55(w -45) = 0

Factor out w - 45

(w - 55)(w -45) = 0

Take any one of the expression and solve for w

w -55 = 0

w = 55

Recall that: l = 100 - w

l =100 - 55

l =45

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Step-by-step explanation:

Mean:

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