ABC is a triangle where AB = 12 cm and AC = 18 cm. 'D' is a point on BC such that BD = CD. If the perimeter of the triangle is 48 cm, then find the length of AD.
Show answer & explanation
Correct answer: D
Explanation
Given:
AB = 12 cm
AC = 18 cm
Perimeter of the triangle = 48 cm
BD = CD
Perimeter = AB + BC + AC
AB + BC + AC = 48
12 + BC + 18 = 48
BC = 48 − 30
BC = 18
Because BD = CD
BD = CD = 18/2 = 9
AD is the median
Formula for the median:
AD² = (2AB² + 2AC² − BC²) / 4
AD² = (2 × 12² + 2 × 18² − 18²) / 4 = 153
AD = √153
= 3√17 cm