Answers

2016-05-06T23:46:25+05:30
Let the side of an equilateral Δ be= x units
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new sides of new Δ=x-12; x-13; x-14.
∵(x-12) side is the longest side in the right angled Δ

∴ACCORDING TO THE PYTHAGORAS THEORAM
(x-13)² + (x-14)²= (X-12)²
after opening the brackets...
x² + 169 - 26x + x² + 196 -  28x = x² +  144 - 24x
2x² + 365 - 54x = x² + 144 -24x
2x²- x² + 365 - 144 - 54x + 24x= 0
x²  - 30x + 221  =0
x² -17x -13x + 221=0
x(x-17) -13(x-17)= 0
(x-13)(x-17)=0
x-13=0  or    x-17=0
x=13              x=17
∵x ≠13                    (because if x is 13 then side (x-13) of Δ would be zero
                                 which is imposiible)
∵x= 17 units
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side of the equlateral Δ is 17 units
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