Question 74

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:

Solution

According to the Problem,

$$BC=2AB-3$$................(1)

$$AC=AB+9$$..................(2)

Perimeter of triangle = 34

$$=$$> $$AB+BC+AC=34$$

$$=$$> $$AB+2AB-3+AB+9=34$$

$$=$$> $$4AB=28$$

$$=$$> $$AB=7$$

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

Share on Whatsapp Share on Whatsapp

Create a FREE account and get: