Question

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 2475 ft2.

Answer 1

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: $l = 100 - w$

$l =100 - 55$

$l =45$