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The perimeter of a triangle is 50 cm one side of a triangle 4cm longer than the smaller side and the third side is 6 CM less than the twice the smaller side find the area of the triangle

Answer»

Step-by-step EXPLANATION:

Let \: the \: smallest \: side \: of \\ \: the \: triangle \: be \: xcm \: long \\ \\ so \: second \: side \: = (x + 4)cm \\ and \: third \: side \: = (2x - 6)cm \\ given \: perimeter \: = 50cm \: \\ therefore \\ x + (x + 4) + (2x - 6) = 50 \\ 4x = 52 \\ x \: = 13 \\ So, \: first \: side \: of \: the \: triangle \: is \: 13cm \\ second \: side \: is \: 17cm \: \\ and \: third \: side \: is \: 20cm \\ \\ Now, \: semi-perimeter \: of \: the \: triangle \\ = \frac{13 + 17 + 20}{2} = \frac{50}{2} = 25cm \\ \\ therofore \: \\ the \: area \: of \: trangle \: \: \\ \delta = \sqrt{s(s - a)(s - b)(s - c)} \\ \delta \: = \sqrt{25(25 - 13)(25 - 17)(25 - 20} \\ \delta = \sqrt{25 \times 12 \times 8 \times 5} \\ \delta = 20 \sqrt{30} {cm}^{2}


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