Question

the length of a rectagle is 5 in longer than its width. if the perimeter of the rectangle is 58 in, find its length and width

Answer 1

Width = 12in, Length = 17in

Explanation:

We can create two expressions from the given statements:

1) L (length) = 5 + W (width)

and

2) 58 = 2L + 2W (the equation for rectangular perimeter)

Substituting L from the first equation into the second equation yields:

58 = 2(5+W) + 2W

Distributing the 2 and solving for W yields:

12in = W

Plug this back into the first expression,

L = 5 + 12

L = 17in

Answer 2

width = 12 in

length = 17 in

Explanation:

Let width of rectangle = x

⇒ length of rectangle = x + 5

Given:

• Perimeter = 58 in

Perimeter = 2 × width + 2 × length

⇒ 58 = 2x + 2(x + 5)

⇒ 58 = 2x + 2x + 10

⇒ 58 = 4x + 10

⇒ 48 = 4x

⇒ x = 12

Therefore,

width = x = 12 in

length = x + 5 = 12 + 5 = 17 in