algebra 2

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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.

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