Acommunity is building a square garden with a walkway around the perimeter with the design shown at the right. find the side length of the inner square that would make the area of the inner square equal to 75% of the total area of the garden. round to the nearest tenth of a foot. 1. what is an expression for the area of the inner square? 2. what is the area of the entire garden? 3. what is 75% of the area of the entire garden? 4. write an equation for the area of the inner square using the expressions from steps 1 and 3. 5. solve the quadratic equation. round to the nearest tenth of a foot. 6. which solution to the quadratic equation best describes the side length of the inner square? explain.

Part 1) An expression for the area of the inner square is

Part 2) The area of the entire garden is

Part 3) 75% of the area of the entire garden is

Part 4) The equation is

Part 5) The solutions of the quadratic equation are

Part 6) The solution that best describes the side length of the inner square is

Step-by-step explanation:

Part 1) What is an expression for the area of the inner square?

we know that

The area of the inner square is equal to

so

Part 2) What is the area of the entire garden?

The area of the entire garden is

Part 3) What is 75% of the area of the entire garden?

we know that

so

Part 4) Write an equation for the area of the inner square using the expressions from Steps 1 and 3

Part 5) Solve the quadratic equation. Round to the nearest tenth of a foot

we have

square root both sides

Part 6) Which solution to the quadratic equation best describes the side length of the inner square?

so

The solution that best describes the side length of the inner square is

because

The side length can not be a negative number

true

step-by-step explanation:

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