Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

What is the side length, s, of the square below?

A blue square labeled A equals 100 meters squared.
Each side of the square measures meters.

===⎯⎯⎯√±=

Convince Me!

Why are there two possible solutions to the equation, X2 = 100? Explain.

Sagot :

sqdancefan

9514 1404 393

Answer:

  x = ±10 m

Step-by-step explanation:

For a square of side length x, the area is given by ...

  A = x²

Your square has an area of A=100, so the equation can be written ...

  100 = x²

Subtracting 100 from both sides gives ...

  x² -100 = 0

and factoring that yields ...

  (x -10)(x +10) = 0

The zero product rule tells us that a product is only zero if one or more factors is zero. The values of x that make these factors zero are ...

  (x -10) = 0   ⇒   x = 10

  (x +10) = 0   ⇒   x = -10

Each side of the square measures 10 meters.

__

There are two possible solutions because the square of a negative number is positive, as is the square of a positive number. (-10)² = 100, just as 10² = 100. There is nothing in the equation that restricts x to positive values.

However, since x is a length equal to the side length of a real geometric object, it cannot have a negative value. So, the only viable answer is x = 10 meters. The solution x = -10 meters is considered to be "extraneous," an artifact of the solution process for the equation.

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.