Question

A fence is to be enclosed around the house. The dimensions of the house are 16 m x 10 m. At least how many metres of fencing are needed?
Please Write All The Steps.​

Answer 1

A backyard farmer wants to enclose a rectangular space for a new garden. She has purchased 80 feet of wire fencing to enclose 3 sides, and will put the 4th side against the backyard fence. Find a formula for the area enclosed by the fence if the sides of fencing perpendicular to the existing fence have length

LIn a scenario like this involving geometry, it is often helpful to draw a picture. It might also be helpful to introduce a temporary variable,

W, to represent the side of fencing parallel to the 4th side or backyard fenceSince we know we only have 80 feet of fence available, we know that

L + W + L = 80, or more simply, 2L + W = 80. This allows us to represent the width, W, in terms of L: W = 80 – 2LNow we are ready to write an equation for the area the fence encloses. We know the area of a rectangle is length multiplied by width, so

A = LW = L(80 – 2L)

A(L) = 80L – 2L2

This formula represents the area of the fence in terms of the variable length

L.

Answer 2

P = 2 × ( l + b )

P = 2 × ( 16 + 10 )

P = 2 × 26

P = 52

Therefore, the number of metres of fencing required is 52.