The base of an isosceles triangle measures 24 cm and its area is 60 cm 2 . Find its perimeter. - Wired Faculty

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Question

The base of an isosceles triangle measures 24 cm and its area is 60 cm². Find its perimeter.

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Solution

Area space equals space straight a over 4 square root of 4 straight b squared minus straight a squared end root rightwards double arrow space space space space 60 24 over 4 square root of 4 straight b squared left parenthesis 24 right parenthesis squared end root rightwards double arrow space space space space 10 equals square root of 4 straight b squared minus 576 end root rightwards double arrow space space space 100 equals 4 straight b squared minus 576 space space space space space space space space space space space space space space space space space space space vertical line space Squaring space rightwards double arrow space space space 4 straight b squared equals 676 rightwards double arrow space space space straight b squared equals 676 over 4 equals 169 rightwards double arrow space space straight b space equals space square root of 169 equals 13 space cm

∴ Perimeter = a + b + b
= 24 + 13 + 13
= 50 cm

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