Question

you are using tiles to make a picture frame for a square photograph with sides 10 inches long. You want the frame to form a uniform border around the photograph, You have enough tiles to cover 300 square inches. What is the largest possible frame width?

Answer 1

let the width of the border be x inches
then
(10+2x)^2 - 100 ≤ 300
100 + 40x + 4x^2 - 100 - 300 ≤ 0
x^2+ 10x - 75 ≤ 0
(x+15)(x-5) ≤ 0
x = 5

So the largest frame is 20 by 20

check: Area of whole frame = 400
area of photo = 100
area of tiles = 300

Answer 2

The largest possible frame width is 17 inches long per side.