The perimeter of a right triangle is 60cm. Its hypotenuse is 25cm.Find the area of the triangle.

Let ABC be a right angled triangle. Since, the perimeter of a right triangle = 60 cm

Thus,

In , Using Pythagoras Theorem,

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LET THE SIDES OF THE TRIANGLE BE a,b,c AND c BE THE HYPOTENUSE 

THEN PERIMETER OF TRIANGLE=a+b+c=60 

                                                              =a+b+25=60

                                                            =a+b=35  (EQ-1)

        BY PYTHAGORAS THEOREM

a^2+b^2=c^2

(a+b)^2-2(ab)=25^2

35^2-2ab=25^2 (PUTING VALUE OF a+b from eq -1)

2ab= 1225-625

ab=6002

ab=300 cm

 NOW AREA OF TRIANGLE =ab2

                                                =150 cm^2

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