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| 1. |
The base of an isosceles triangle measures 80cm and Find the perimeter of triangle |
| Answer» Let each equal side be a cm and base = 80 cmArea =\xa0{tex}\\frac { 1 } { 4 } b \\times \\sqrt { 4 a ^ { 2 } - b ^ { 2 } }{/tex}\xa0sq. units=\xa0{tex}\\frac { 1 } { 4 } \\times 80 \\times \\sqrt { 4 a ^ { 2 } - 6400 }{/tex}\xa0cm2=\xa0{tex}20 \\times \\sqrt { 4 a ^ { 2 } - 6400 }{/tex}\xa0But area = 360 cm2{tex}\\therefore 20 \\sqrt { 4 a ^ { 2 } - 6400 }{/tex} = 360{tex}\\Rightarrow 20 \\times 2 \\sqrt { a ^ { 2 } - 1600 }{/tex}\xa0= 360{tex}\\Rightarrow \\sqrt { a ^ { 2 } - 1600 } = 9{/tex}{tex}\\Rightarrow a ^ { 2 } - 1600{/tex}\xa0= 81{tex}\\Rightarrow a ^ { 2 } = 1681{/tex}{tex}\\Rightarrow{/tex}\xa0a = 41 cm{tex}\\therefore{/tex}\xa0perimeter of triangle = (2a + b) cm= (2\xa0{tex}\\times{/tex}\xa041 + 80) cm= (82 + 80) cm = 162 cmHence, perimeter of the triangle = 162 cm | |