Q1. THE PERIMETER OF AN ISOSCELES TRIANGLE IS 36CM AND HEIGHT IS 12CM, THEN FIND ITS AREA.
SOL:- AB = AC, BC = BD + DC
AB+ AC + BC =36 CM .AB +AB +BC = 36 CM
2AB + 2BD = 36CM.
2( AB + BD) = 36 CM.
AB + BD = 18 CM .......................1
NOW PYTHAGORAS'S THEOREM.
AB^2 = AD^2 + BD^2
AB^2 - BD^2 = AD^2.
( AB+BD )( AB -BD) = 12^2
18 CM (AB - BD) = 144
AB- BD = 144/18
AB - BD = 8 CM ................................2.
FROM EQUATION 1 & 2
AB + BD = 18 CM
AB - BD = 8 CM
.................................................................................
2AB = 26 CM
AB = 13 CM , AC = 13 CM , BC = 36 CM - 26CM = 10CM.
AREA OF THIS TRIANGLE = 1/2 BASE . HEIGHT
= 1/2 10 CM . 12 CM.
= 5 CM .12 CM
= 60 CM^2
.
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