The length of a rectangle is five less than the twice the width. The perimeter of the rectangle is 70 inches. Find the length and width

Question

please help I’m really struggling with this

Answer 1

Let L = length

Let W = width.

"length of a rectangle is 5 less than twice the width" can be written as L = 2W - 5

Perimeter Formula = 2L + 2 W = 2(L +W)

 

Set up formula.

70 = 2( L + W).

Substitute L = 2W - 5

70 = 2(2W -5 + W)

Combine like terms.

70 = 2(3W - 5)

Divide both sides by 2. (Or, you can distribute the 2 across the 3W -5. You will get the same end answer either way).

35 = 3W - 5

Add 5 to both sides.

40 = 3W.

Divide both sides by 3.

W = 40/3 ≈ 13.33

Now that we have the width, plug this back in to find the length.

L = 2W - 5

Replace W with 40/3 and simplify

L = 2(40/3) - 5 = 80/3 - 5 = 65/3 ≈ 21.66

 

So,

W = 40/3 ≈ 13.33

L =  65/3 ≈ 21.66