John is building a fence around his home. Currently his fence measures 14 feet on each side but he wants to increase only the width of his fence by x feet to have a rectangular fence that has an area of 280 square feet. Write an equation that can be used to find x then solve your equation

The value of x is 6 feet.

Step-by-step explanation:

Area of rectangle = lengthwidth

280 = (14) (14+x)

280/14 =  14+x

20 = 14+x

x = 20-14

x = 6 feet

The width of the rectangular fence is (14+x) = 20 feet.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

l.jnl.j/n.m,lm,

step-by-step explanation: