In a triangle, if the longest side has a length of 15 cm, one of another side a length of 12 cm, and its perimeter is 34 cm, then the area of the triangles in cm2 is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e.
Given that
The sides of the triangle a = 15 cm, b = 12 cm
Let the other side of the triangle be c cm
the perimeter of the triangle is 34 cm
Formula used
The semi perimeter (s ) = (a + b + c)/2
The area of the triangle = √[s × (s – a) × (s – b) × (s – c)]
Calculations
The semi perimeter = 34/2 = 17 cm
34 = a + b + c
c = 34 - 15 - 12 = 34 - 27 = 7 cm
The area of the triangle = √[17 × (17 – 15) × (17 – 12) × (17 – 7)]
= √[17 × 2 × 5 × 10]
= √1700 = 10√17 cm2