The area of grandiose rectangular painting is 56 in.² the width of the painting is 7 inches what The area of grandiose rectangle or painting is 56 in.² the width of the painting is 7 inches label the rectangle to represent the paying

Complete Question

The area of grandiose rectangular painting is 56 in.² the width of the painting is 7 inches what is the diagonal of the painting

The diagonal of the rectangular painting is  

Step-by-step explanation:

The diagram for this question is shown on the first uploaded image

From the question we are told that  

    The area is

    The width of the painting is

Generally the area of the rectangle is mathematically represented as

where the length which is mathematically evaluated as

substituting value  

According Pythagoras theorem

Where z is the diagonal of the rectangular painting

  Now substituting values

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12