Question

A shop sells fence panels with a wooden frame going all the way round each panel. The price of each panel is based on the area of the panel and the length of the wooden frame around the panel.

Use the prices given given in the attachment to find out how much the shop charges per square metre of the panel and per metre for the wooden frame .

a) Each 1m² of fence panel costs:?
b) I metre of wooden frame costs:?

Plz answer this question. ​

Answer 1

a) Each 1m² of fence panel costs: £2

b) I metre of wooden frame costs: £1

Explanation:

Let the price of 1 sq.m. of fence panel be x

Let the price of 1 m of wooden frame be y

In Fig 1

Length = 4 m

Breadth = 3 m

Area =
`Length * breadth = 4 * 3 = 12 sq.m.`

Cost of 1 sq.m. = x

Cost of 12 sq.m. = 12x

Perimeter =2(l+b)=2(4+3)=14 m

Cost of 1 m of wooden frame = y

Cost of 14 m of wooden frame = 14y

We are given that total cost of framing and fencing is 38

So. 12x+14y=38 ----1

In Fig 2

Length = 6 m

Breadth = 2 m

Area =
`Length * breadth = 6 * 2 = 12 sq.m`.

Cost of 1 sq.m. = x

Cost of 12 sq.m. = 12x

Perimeter =2(l+b)=2(6+2)=16 m

Cost of 1 m of wooden frame = y

Cost of 16 m of wooden frame = 16y

We are given that total cost of framing and fencing is 40

So. 12x+16y=40---2

Substitute the value of 12x form 1 in 2

38-14y+16y=40

2y=2

y=1

Substitute the value of y in 2

12x+16=40

12x=24

x=2

So, cost of 1 sq.m. of fence panel is 2 and cost of 1 m of wooden frame is 1

In fig 3

To verify :

Length = 3 m

Breadth = 5 m

Area =
`Length * breadth = 3 * 5 = 15 sq.m.`

Cost of 1 sq.m. = 2

Cost of 12 sq.m. =
`15 * 2 = 30`

Perimeter =2(l+b)=2(3+5)=16 m

Cost of 1 m of wooden frame = 1

Cost of 16 m of wooden frame = 16

So, Total cost = 30+16=46

We are given that cost of fencing and framing is 46

Thus verified

Hence

a) Each 1m² of fence panel costs: £2

b) I metre of wooden frame costs: £1