Question

The width of a photo is 5 inches less than its length. A border of 2 inches is placed around the photo. The area covered by the photo and its border is 104 square inches. Find the dimensions of the photo itself

Answer 1

Answer:

Dimensions of photo excluding border:

x = 11 inches

y = 6 inches

Step-by-step explanation:

Let the length be 'x' and width be 'y'.

The width of a photo is 5 inches less than its length, that is:

x-5 = y

let 'X' be length of photo including border and 'Y' be the width of photo including border:

Where X = x+2 and Y = y+2

Now , we have X-5 = Y

and X*Y = 104 square inches

*putting Y = X-5*

X(X-5) = 104

$X^2 - 5X - 104 = 0$

$X^2 - 13X + 8X - 104 =$

$X(X-13)+8(X-13) = 0\\(X-13)(X+8)$

⇒ X-13 = 0          or        X+8 = 0

Hence X = 13       or X = -8

As length can not be negative, X = 13 inches

Y = X-5 = 13-5 = 8 inches

Dimensions of photo excluding border:

x = X - 2 = 13-2 = 11 inches

y = Y-2   =  8-2 =  6 inches