In triangle ABC, the length of BC is less than twice the length of AB by 3 cm. The length of AC exceeds the length of AB by 9 cm. The perimeter of triangle is 34 cm. The length (in cm) of the smallest side of the triangle is:
According to the Problem,
$$BC=2AB-3$$................(1)
$$AC=AB+9$$..................(2)
Perimeter of triangle = 34
$$=$$>Â $$AB+BC+AC=34$$
$$=$$> $$AB+2AB-3+AB+9=34$$
$$=$$> $$4AB=28$$
$$=$$>Â $$AB=7$$
From (1), $$BC=2\left(7\right)-3=11$$
From (2), $$AC=7+9=16$$
$$\therefore\ $$The length of the smallest side of the triangle is $$AB=7cm$$
Hence, the correct answer is Option D
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