Mathematics

Question

Find the length of the missing side of a rectangle if the diagonal is 13 cm and the shortest side is 5cm​

And please show the steps and explain

1 Answer

  • Answer:

    12 cm

    Step-by-step explanation:

    I drew a picture of a rectangle with a diagonal measurement of 13 units and what appear to be the shortest side to be 5 units. (This picture was not drawn to scale.) We were has to find the longest side which I said was b. Notice the diagonal cuts the rectangle into right triangles.

    We will need to use Pythagorean Theorem to find the length of the longer side of the rectangle.

    [tex]5^2+b^2=13^2[/tex]

    [tex]25+b^2=169[/tex]

    Subtract 25 on both sides:

    [tex]b^2=144[/tex]

    Take square root of both sides:

    [tex]b=\sqrt{144}[/tex] (I did not worry about the negative answer to this because we are dealing with lengths.)

    [tex]b=12[/tex]

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