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

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`

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`