find the area of an isosceles triangle measure 24cm and its area is 192cm.find its perimeter
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Let ABC is an isosceles triangle,in which AB= AC =a cm and the base (b)= 24 cm
A/q
The are of an isosceles triangle
=(b/4)×√(4a²-b²) [since,A=(b/4)√(4a²-b²) ,and altitude (h)=(1/2)√(4a²-b²) ]
=>192=(24/4)×√[4a²-(24)²]
=>192=6×√[4a²-576]
=>192/6=√[4a²-576]
=>32=√[4a²-576]
=>(32)²=4a²-576
=>1024+576=4a²
=>1600==4a²
=>1600/4=a²
=>a²=400
=>a=√400
Therefore, a=20 cm
Hence, the perimeter of the isosceles triangle ABC=AB+BC+AC
=a+b+a
=20+24+20
=64 cm, Ans.
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