Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

The length of a certain rectangle is 6 meters more than twice its width. What is the perimeter of the rectangle if the area of the rectangle is 260 square meters?​

Sagot :

rvkacademic

Answer:

Perimeter = 72 meters

Step-by-step explanation:

Let L be the length and W the width of the rectangle

We have the following relationship

L = 2W + 6

Area of the rectangle = LW = (2W+6)W   by substituting for L

Area =

2W² + 6W =260 ==> 2W² + 6W -260 = 0

Dividing both sides by 2 yields

W² + 3W -130 = 0

This is a quadratic equation which can be solved using the formula for the roots of the equation ie the values of W which satisfy the above equation

However in this case it is easier to solve by factorization

W² + 3W -130  

= W² + 13W - 10W - 130
= W(W + 13) -10(W + 13)

= (W+13)(W-10) = 0

This means W is either -13 or W = 10

Since W cannot be negative, we get W = 10 and

L = 2(10) + 6 = 26

Perimeter of a rectangle is given by

2(L + W) = 2(26 + 10) = 2(36) = 72  Answer

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.