Arectangular piece of plywood has a diagonal which measures two feet more than the width. the length of the plywood is twice the width. what is the length of the plywood’s diagonal? round your answer to the nearest tenth.

The length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4

Step-by-step explanation:

let l be the length and w be the width of the rectangle respectively;

Diagonal(D) of a rectangle is given by:

                             ......[1]

As per the given statement we have;

Diagonal(D) = width + 2

and

= 2w

Now, substitute these in  [1] we have;

Squaring both the sides we get;

or

or

Simplify:

                        ......[2]

The quadratic equation is in the form  of

the solution is given by:  

On comparing with [1] we get

a= 1 , b = -1 and c = -1

Then the solution is:

Simplify:

and

Then, the diagonal D = w+2

For

For

therefore, the length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4

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!