Triangle ABC is an isosceles triangle, with AB=AC, altitude AM=11cm. Let a point D be on AM so that AD=10cm. If angleBDC=3× angleBAC. The perimeter of the triangle is?
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Explanation:
The figure is as shown in the attached image.
sinB=
AB
10
=
BC
12
⇒BC=1.2AB=1.2AC
sin
2
A
=
AB
BD
=
AB
2
BC
=
AB
0.6AB
=0.6
⇒cos
2
A
=0.8andtan
2
A
=
0.8
0.6
=
4
3
⇒
AD
BD
=
4
3
⇒BD=10×
4
3
=7.5
BC=2×BD=15
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