In a triangles ABC, the length of the side AC is 4 cm more than 2 times the length of the side AB. Length of the side BC is 4 cm less than the three times the length of the side AB. If perimeter of △ABC is 60 cm, than its area (in cm2 ) is :
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 120
Let AB be x cm then BC becomes 2x + 4 and AC becomes 3x - 4
Perimeter of ABC = 60
x + 2x + 4 + 3x - 4 = 60
6x = 60
x = 10.
The side of the triangle becomes 10, 24 and 26.
10 - 24 - 26 is a Pythagorean triplet means ABC is a right-angle triangle.
Area of the triangle = 1/2 × 24 × 10 = 120 cm2.