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Equilateral triangles are drawn on the …

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Equilateral triangles are drawn on the sides of a right triangle . Show that area of the triangle on the hypotenuse is equal to the sum of the areas of the triangles on the other two sides.

    • Posted by Rohit Verma 6 years, 9 months ago

    CBSE > Class 10 > Mathematics
    • 2 answers

    Shikhar Singh 6 years, 9 months ago

    This question can be solve with pythagoras theorem in very few steps.

    1Thank You

    Gaurav Seth 6 years, 9 months ago

    Equilateral triangles are drawn on the sides of a right-angle triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

    <hr />

    Given: A right-angle triangle right angled at B. Three equilateral triangles ABE, BCF and ACD are described on sides AB, BC and AC respectively.

    To Prove:  ar(∆ACD) = ar(∆ABE) + (∆BCF)
    Proof:    ∵ All triangle are equilateral therefore, by using AAA condition.
                       
    When  then
                  
            
                            [Taking reciprocal of both sides]
    When , then
                              ...(ii)
    Adding (i) and (ii), we get
      

        

           

         

    0Thank You

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