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

 Given, the perimeter of right triangle $=60\text{ }cm$ and hypotenuse $=25\text{ }cm$ $\therefore AB+BC+CA=60\text{ }cm$ $AB+BC+25=60$ $\therefore AB+BC=35$                                                            ?(i) Now, by pythagoras theorem, ${{(AC)}^{2}}={{(AB)}^{2}}+{{(BC)}^{2}}$ ${{(25)}^{2}}={{(AB)}^{2}}+{{(BC)}^{2}}$ $\therefore A{{B}^{2}}+B{{C}^{2}}=625$                                                   ?(ii) we, know that, ${{(a+b)}^{2}}={{a}^{2}}+{{b}^{2}}+2ab$ then,               ${{(AB+BC)}^{2}}\text{=(}AB{{)}^{2}}+{{(BC)}^{2}}+2AB.BC$ ${{(35)}^{2}}=625+2AB.BC$ $\therefore 2AB.BC=1225-625$ $2AB.BC=600$ $\therefore AB.BC=300$ $\therefore$      Area of $\Delta \text{ }ABC=\frac{1}{2}~\times AB\times BC$ $=\frac{1}{2}\times 300=150\,\,c{{m}^{2}}$