Algebra Question - Question in description

Question

An electricity facility has three square solar panel fields. The diagram shows their arrangement and areas (in square meters). * The diagram has three boxes and the first box contains 4x^2 + 40x + 100 and the second box contains x^2 and the third box contains x^2 + 40x + 400. 

 

a.) How many meters longer is the side length of box 3 than the side length of box 2? Explain how you found your answer. (Hint: you need to find the side lengths of each box first)

 

b.) For what value of x is the area of box 1 equal to the combined area of box 2 and box 3?

 

c.) The length of box 1 is 10 meters longer than the side length of Grid 3. What is the total area of three grids? Explain how you found your answer.

 

*P.S.    I only want the answers and the work. I just want to check my answers. Thanks

 

Answer 1

(a) Let's find the side lengths of each box. Since these boxes are square, and Area = side², we can take the square root of the area to find the length of a side. Factor each equation:

 

4x² + 40x + 100

(2x + 10)(2x + 10)

(2x + 10)²

 

First box's side length: 2x + 10 meters

 

x²

 

Second box's side length: x meters

 

x² + 40x + 400

(x + 20)(x + 20)

(x + 20)²

 

Third box's side length: x + 20

 

So, how many meters longer is the third box than the second box? Subtract:

 

(x + 20) - x

x + 20 - x

20 meters

 

 

(b) Let's set the area of box 1 equal to the areas of box 2 and 3 and solve for x:

 

4x² + 40x + 100 = x² + x² + 40x + 400

4x² + 40x + 100 = 2x² + 40x + 400

2x² + 40x + 100 = 40x + 400

2x² + 100 = 400

2x² = 300

x² = 150

x = √150 ≈ 3.87 meters

 

 

(c) By "Grid 3," I'll assume you just mean box 3.

 

The length of box 1 is 10 meters longer than the length of box 3. So:

 

2x + 10 - 10 = x + 20

2x = x + 20

x = 20

 

Plug x = 20 into each area equation and sum them together:

 

4(20)² + 40(20) + 100 + (20)² + (20)² + 40(20) + 400

4(400) + 800 + 100 + 400 + 800 + 400

1600 + 900 + 1200 + 400

2500 + 1600

4100 square meters