Answered

Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

A shed has dimensions of 12m in length and 5 m in width. Both the length and width are increased by the same amount in order to increase the floor area by more than double the original area?

Sagot :

The amount by which the length and width of a shed can be increased to

more than double the area, depends on the initial dimensions.

  • The amount that can be added to both the length and the width to increase the floor area by more than double the original area is more than 3 meters.

Reasons:

The given parameters of the shed are;

The length of the shed = 12 m

Width of the shed = 5 m

The amount by which the length and the width are increased = The same amount

The new area after the increase in the length and width of the shed = More than double the initial area

Required:

The amount of increase in the length.

Solution:

Let the amount by which the length and width are increased = x

We have;

Initial area of the shed = 12 m × 5 m = 60 m²

The new area = (12 + x) × (5 + x) > 2 × 60

By multiplication, we get;

(12 + x) × (5 + x) = x² + 17·x + 60 > 2 × 60 = 120

x² + 17·x + 60 - 120 > 120 - 120 = 0

x² + 17·x - 60 > 0

By factorization, we get;

(x + 20)·(x - 3) > 0

x > -20, or x > 3

The increase (positive) amount of the solution is x > 3

Therefore, the amount by which both the length and the width can be increased to more than double the area is x > 3 meters

Learn more about the area of a rectangle here:

https://brainly.com/question/16410706

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.