Posted by **jasmin** on Thursday, December 29, 2011 at 3:29pm.

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?

- algebra 2 -
**Reiny**, Thursday, December 29, 2011 at 4:33pm
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

- algebra 2 -
**Eric**, Thursday, December 29, 2011 at 4:34pm
The largest possible frame width is 17 inches long per side.

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