A rectangle has a diagonal length of 5cm and one side with length 3cm. Find the area of the rectangle.

Question

A rectangle has a diagonal length of 5cm and one side with length 3cm. Find the area of the rectangle.

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Alexandra 2 weeks 2021-09-12T13:38:59+00:00 1 Answer 0

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    2021-09-12T13:40:48+00:00

    Answer:

       Area of the rectangle is 12cm^2

    Step-by-step explanation:

    Given:

    Diagonal= 5 cm

    Length=3 cm

    The diagonal of a rectangle cuts it into two equal Right triangles, where the length of the third side can be found by using the Pythagorean theorem i.e:

    Hypotenuse^2=Perpendicular^2+Base^2

    The diagonal is the hypotenuse of the triangle as its the longest side of the triangle formed:

    Diagonal^2=Length^2+Width^2\\

    5^2=3^2+Width^2

    25=9+width^2

    width^2=25-9

    width^2=16

    Width=\sqrt{16} \\

    Width=4 cm

    Area of a rectangle= length*Width

                                 = 3cm * 4cm\\\\Area=12cm^2

    Area of the rectangle is 12cm^2

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