Question

A rectangular lot whose perimeter is 380 ft is fenced along three sides. An expensive fencing along the​ lot's length cost $ 25 per foot. An inexpensive fencing along the two side widths costs only $ 5 per foot. The total cost of the fencing along the three sides comes to $ 3625. What are the​ lot's dimensions?

Answer 1

We have two widths of the same length plus one length

Let the width be $w$ and the length be $l$

Perimeter = 2×width + 2×length
$380 = 2w + 2l$
 $380 = 2(w+l)$
$190 = w+l$(equation 1)

The cost is $5 per foot on the width and $25 per foot on the length
Total cost = (5 × 2 × width) + (25 × length)
$3625 = 10w + 25l$ (equation 2)

We have two variables that we need to solve, so we will need to use the simultaneous equations method (either elimination or substitution)

Since equation 1 is given $190 = w + l$, we can rearrange the equation to make $l$ the subject

$l=190-w$

then substitute this into equation 2

$3625 = 10w + 25l$
$3625=10w + 25(190-w)$
$3625=10w+4750-25w$
$3625=-15w+4750$
$15w = 4750 - 3625$
$15w = 1125$
$w = 1125/15$
$w = 75$

Substitute w = 75 back into 190 = w + l

190 = 75 + l
l = 190 - 75
l = 115

Answer:
Length = 115 feet
Width = 75 feet