Question

The length of a rectangle is 5/2 units greater than twice its width. If its width is w, which expression gives the perimeter of the rectangle in terms of w?
1. 2(5/2w) + w
2. 5/2w + w
3. 3w + 10/2
4. 6w + 5

Answer 1

L=5/2*2w=5w
P=(5w+w)*2=12w
Perimeter is 12w

Answer 2

Answer:

Option 4 is correct

$P=5+6w$

Step-by-step explanation:

Perimeter of a rectangle is given by:

$P=2(l+w)$            ....[1]

where w be the width of the rectangle and l be the length of the rectangle.

As per the statement:

length of a rectangle is 5/2 units greater than twice its width.

⇒ $l = \frac{5}{2}+ 2w$ units

Substitute this in [1] we get;

$P=2(\frac{5}{2}+ 2w+w)$

Combine like terms;

$P=2(\frac{5}{2}+3w)$

Using distributive property: $a\cdot (b+c) =a\cdot b+ a\cdot c$

$P=5+6w$

Therefore, the perimeter of the rectangle in terms of w is $P=5+6w$ units