Question

The perimeter of the rectangle is 28 units.
what is the value of w? ​

Answer 1

5

Explanation:

Since this is a rectangle, opposite sides are congruent.

That is, the perimeter in terms of w is:

(2w-1)+(2w-1)+(w)+(w)

or

2(2w-1)+2(w)

We can simplify this.

Distribute:

4w-2+2w

Combine like terms:

6w-2

We are given that the perimeter, 6w-2, is 28.

So we can write an equation for this:

6w-2=28

Add 2 on both sides:

6w =30

Divide both sides by 6:

w =30/6

Simplify:

w =5

w is 5

Check if w=5, then 2w-1=2(5)-1=10-1=9.

Does 5+5+9+9 equal 28? Yep it does 10+18=28.

Answer 2

w=5

Explanation:

To find the perimeter of the rectangle

P = 2(l+w)

where w is the width and l is the length

Our dimensions are w and 2w-1 and the perimeter is 28

Substituting into the equation

28 = 2(2w-1 +w)

Combining like terms

28 = 2(3w-1)

Divide each side by 2

28/2 = 2(3w-1)/2

14 = 3w-1

Add 1 to each side

14+1 = 3w-1+1

15 = 3w

Divide each side by 3

15/3 =3w/3

5 =w