Ava asked in Science & MathematicsMathematics · 6 months ago

How long is a side of the original square banner?

A square banner had 4 feet added its width and 2 feet subtracted from its height. The banner then had an area of 91 square feet. How long was a side of the original square banner?

4 Answers

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  • RR
    Lv 7
    6 months ago

    A square banner (call sides x)

    ...had 4 feet added its width

    x + 4

    ...and 2 feet subtracted from its height.

    x - 2

    The banner then had an area of 91 square feet.

    (x+4)(x -2) = 91

    x^2 +2x - 8 = 91

    x^2 + 2x -99 = 0

    factorise

    (x + 11)(x - 9) = 0

    x = - 11 (reject negative value)

    x = 9 feet

  • 6 months ago

    91 = 7 * 13 (prime factors)

    The side was originally 7+2 = 13-4 = 9 feet long.

  • Mike G
    Lv 7
    6 months ago

    x = original side length in ft

    (x+4)(x-2) = 91

    x^2+2x-99 = 0

    (x+11)(x-9) = 0]

    x = 9 ft

  • david
    Lv 7
    6 months ago

    (x+4)(x-2) = 91

    x^2 + 2x - 99 = 0

    (x+11)(x-9) = 0

    x = 9 <<< answer

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