Question

Katie wants to create a rectangular frame for a picture. She has 60 inches of material. If she wants the length to be 3 more than 2 times the width what is the largest possible length

Answer 1

Largest possible length is 21 inches.

Explanation:

Given:

Total material available = 60 inches

Length to be 3 more than twice of width.

To find:

Largest possible length = ?

Solution:

As it is rectangular shaped frame.

Let length =
`l` inches and

Width =
`w` inches

As per given condition:

`l = 2w+3` ..... (1)

Total frame available = 60 inches.

i.e. it will be the perimeter of the rectangle.

Formula for perimeter of rectangle is given as:

`P = 2 * (Width + Length)`

Putting the given values and conditions as per equation (1):

`60 = 2 * (w+ l)\\\Rightarrow 60 = 2 * (w+ 2w+3)\\\Rightarrow 60 = 2 * (3w+3)\\\Rightarrow 30 = 3w+3\\\Rightarrow 3w = 27\\\Rightarrow w = 9 \ inch`

Putting in equation (1):

`l = 2* 9+3\\\Rightarrow l = 21\ inch`

So, the answer is:

Largest possible length is 21 inches.