# algebra 2

posted by .

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 -

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 -

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

## Similar Questions

1. ### Math

You are using glass 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 …
2. ### math

a picture frame containing a photogragh is 11 inches wide and 14 inches high. a mat around the photograph is 1 1/2 inches wide on all sides. what are the dimensions of the photograph?
3. ### algebra

a square photograph measuring 8 inches by 8 inches is positioned within a 1 inch wide picture frame as best shown. select the best answer. what is the combined area of the photograph and frame?
4. ### Math

A photograph measuring 8 inches by 6 inches is surrounded by a mat. The mat has the same width on all sides of the photograph. The photograph and mat are put into a glass photo frame which just covers the outside of the mat. If the …
5. ### math

A photograph measuring 8 inches by 6 inches is surrounded by a mat. The mat has the same width on all sides of the photograph. The photograph and mat are put into a glass photo frame which just covers the outside of the mat. If the …
6. ### Algebra

The floor of a rectangular room will be tiled with square tiles that measure 3 inches on each side. The room is 109 inches long and 103 inches wide. How many tiles, including parts of tiles, are needed to complete the job?