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

Answer:

Largest possible length is 21 inches.

Step-by-step 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:

$P = 2 \times (Width + Length)$

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

$60 = 2 \times (w+ l)\\\Rightarrow 60 = 2 \times (w+ 2w+3)\\\Rightarrow 60 = 2 \times (3w+3)\\\Rightarrow 30 = 3w+3\\\Rightarrow 3w = 27\\\Rightarrow w = 9 \ inch$

Putting in equation (1):

$l = 2\times 9+3\\\Rightarrow l = 21\ inch$

So, the answer is:

Largest possible length is 21 inches.