In triangle ABC, the length of side BC is 2 cm less than twice the length of side AB. The length of side AC exceeds the length of side AB by 10 cm. The perimeter of the triangle is 40 cm. Determine the length (in cm) of the smallest side of the triangle.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 8.
Given that, BC = (2AB - 2) cm
AC = (AB + 10) cm
Perimeter of triangle ABC = 40 cm
According to the given question,
AB + BC + AC = 40
⇒ AB + 2AB - 2 + AB + 10 = 40
⇒4AB = 40 - 8
⇒ 4AB = 32
⇒ AB = 8
Now, BC = 14 cm and AC = 18 cm
Hence the length (in cm) of the smallest side of the triangle is 8.