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Answer:
The equal sides of an isosceles triangle are 20 cm and its area = 192 sq cm.
Let the base angles be m.
The area of the triangle = [2*20 cos m * 20 sin m]/2 = 192, or
400 sin m cos m = 192, or
200 [2 sin m cos m] = 192, or
2 sin m cos m = 192/200 = 0.96, or
sin 2m = 0.96, or
2m = arc sin 0.96 = 73.73979529, or
m = 73.73979529/2 = 36.86989765 deg.
The base of the triangle = 2 * 20 cos 36.86989765 = 32 cm.
Hence the perimeter of the isosceles triangle = 20*2+32 = 72 cm.
Check: 2s = 72, or s = 36.
Area of isosceles triangle = [36{36–32)(36–20)(36–20]^0.5
= [36*4*16*16]^0.5 = 6*2*16 = 192 sqUARE cm.
Step-by-step explanation:
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