Question

# A square icon image has a border that has an area of 704 square pixels and is 4 pixels wide. What is the area of the square image?

Hint:

### The methods used to find the product of binomials are called special products.

Multiplying a number by itself is often called squaring.

For example (*x* + 3)(*x* + 3) = (*x* + 3)2

Area of square = (side)2

## The correct answer is: 7396

### Area of the border = Area of the square of x+4 side - Area of the square of side x

= (x + 4)^{2} - x^{2}

= (x + 4)(x + 4) - x^{2}

= x(x + 4) + 4(x + 4) - x^{2}

= x(x) + x(4) + 4(x) + 4(4) - x^{2}

= x^{2} + 4x + 4x + 16 - x^{2}

= 8x + 16

The area of the border is given as 704 square pixels

So, 8x + 16 = 704

8x = 704 - 16

x = 86 pixel

Area of the square image = x^{2}

= 86^{2} = 7396 square pixels

Final Answer:

Hence, the area of the square image is 7396 square pixels

^{2}- x

^{2}

^{2}

^{2}

^{2}

^{2}+ 4x + 4x + 16 - x

^{2}

The area of the border is given as 704 square pixels

Area of the square image = x

^{2}

= 86

^{2}= 7396 square pixels

Final Answer:

Hence, the area of the square image is 7396 square pixels

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