Question

A photo is printed on a 5-inch by 7-inch piece of paper. The photo covers 24 square inches and has a uniform border. what is the width of the Border?

Answer 1

Answer: The width of the border is 1 inch

Explanation:

The area of the paper is

A = 5 in* 7in = 35 in^2

The area of the photo is 24 in^2

The difference in the area is 35 in^2 - 24in^2 = 11in^2

knowing that the inside area is of 24 in, we can write it as a product of two numbers, let's use x*y = 24

then we have that:

(7 -x)*(5 - x) = 24

where x is the width of the borders.

35 - 5x - 7x + x^2 = 24

x^2 - 12x + 11 = 0

the solutions are for this quadratic equation are:

`x = (12 +- √(12^2 - 4*11*1) )/(2) = (12 +-10 )/(2)`

so we have two solutions

x = (12 + 10)/2 = 11

this can not be the correct option, because the border will be larger than the actual paper, so we can discard this solution of the quadratic equation.

x = (12 - 10)/2 = 1

this is the correct answer, we found that the width of the border is 1 inch.

then we have:

(7 in - 1 in)*(5 in - 1in) = 6in*4in = 24in^2