Question

a rectangle field is to be enclosed with 1140ft of fencing. if the length of the field is 70ft longer than the width, then how long is the field?

Answer 1

length = 320 ft

Explanation:

Framing algebraic equations and finding the unknown value:

Let the width of the rectangle field = x ft

length = (x + 70) ft

Perimeter = 1140 ft

We know that,

`\boxed{\bf Perimeter \ of \ rectangle = 2*(length + width)}`

2* (length + width) = 1140

2*(x + x + 70) = 1140

Combine like terms,

2*(2x + 70) = 1140

Open the parenthesis, by multiplying each term inside the parenthesis by 2,

2*2x +2*70 = 1140

4x + 140 = 1140

Subtract 140 from both sides,

4x = 1140 - 140

4x = 1000

Divide both sides by 4,

x = 1000 ÷ 4

`\boxed{\bf x = 250 \ ft}`

Length of the rectangle field = 250 + 70

= 320 ft

Answer:

Length = 320 ft