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what is the longest side of the rectangle?

A rectangle measures x+10 cm and x-10 cm, squares of side 3 cm are taken from each corner. The resulting shape has an area 264cm2. Find the length of the longest side of the rectangle

3 Answers

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  • Jim
    Lv 7
    1 month ago

    Total area = 264cm² + 2*(3cm x 3 cm) = 283 cm²

    283 cm² = (x+10 cm) (x-10 cm) = x² -100

    x = √383

    x + 10 = 10 + √383 cm = 29.57 cm

  • 1 month ago

      A rectangle measures (x + 10) cm by (x - 10) cm. 

      Squares of side 3 cm are taken from each corner.  

      The resulting shape has an area of 264 cm^2. 

      (x + 4)(x - 16) = 264

      x^2 - 12x - 328 = 0

      x ≈ 25.079 cm

      The length of the longest side of the rectangle is 25.079 cm.

  • 1 month ago

    A(rectangle) = ( x + 10)(x - 10) = x^2 - 100 

    The four corners are 4 x 3 x 3 = 36cm^2 

    Hence 

    x^2  - 100 - 36 = 264

    x^2 = 136 + 264  

    x^2 = 400 

    x = +/-20 

    x = 20 

    Hence longest side is 20 + 10 = 30 cm 

    & shortest side is 20 - 10 = 10 cm  

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