Question

The width of a rectangle field is 3h yards and its length is 3 yards longer than the width. The field has a fence around its perimeter with a gate 4 yards wide as shown below. Right in expression for the perimeter of the rectangular fields in terms of h excluding the width of the gate

Answer 1

Answer:

Part a) $P=(12h+2)\ yd$

Part b) The expression that represent the cost of fencing the field is $(336h+56)$

Part c) $\ 1,736$

Step-by-step explanation:

The complete question in the attached figure

Part a) we know that

The perimeter of the rectangular field (excluding the width of the gate) is equal to

$P=2(L+W)-4$

we have

$L=(3h+3)\ yd\\W=3h\ yd$

substitute the given values

$P=2(3h+3+3h)-4$

$P=2(6h+3)-4\\P=12h+6-4\\P=(12h+2)\ yd$

Part b) we know that

To find out the cost of fencing the field (excluding the gate) , multiply the perimeter by the cost of $28 per yard

so

$28(12h+2)=336h+56$

Part c) we have

h=5

substitute the value of h in the expression of the cost

$336(5)+56=\ 1,736$