The width of a rectangle is 2 less than its length. if the perimeter of the rectangle is no more than30 centimeters, find the range of possible lengths and widths of the rectangle. use the formula, p=2l+2w, for the perimeter of the rectangle. in the form of a paragraph, explain in complete sentences the steps necessary to set up the equation. include the final inequality in your explanation. complete your work in the space provided or upload a file that can display math symbols if your work requires it.

We will take length as variable l and width as variable w.

Formula for perimeter of the rectangle is P=2(l+w)

and l=w+2 and P≤30

First we replace l in formula for perimeter and get this inequality

2(w+2+w)≤30, than we divide this inequlity with 2 and get 2w+2≤15 =>

2w≤13 => w≤6.5

When we replace w in formula for l we get

l-2 ≤ 6.5 => l≤6.5+2 => l≤8.5

If you need some more explenation I am here

good luck!!!

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation: