In a triangle ABC, the length of side AC is 4 cm less than five times the length of side AB. The length of side BC exceeds four times the length of side AB by 4 cm. If the perimeter of ΔABC is 90 cm, then its area is: |
160 cm2 164 cm2 180 cm2 148 cm2 |
180 cm2 |
We know that, If a, b and c are the sides of a triangle then, Area of triangle = √{s(s -a) (s -b) (s - c)} where s is semi perimeter of triangle = (a + b + c)/2 We have, AC = (5AB - 4) cm BC = (4AB + 4)cm AB + BC + AC = 90 cm Let the side AB is x cm According to the question, AB + BC + AC = 90 = x + (4x + 4) + (5x - 4) = 90 = 10x = 90 = x = 9 BC = 4(9) + 4 = 36 + 4 = 40 AC = 5(9) - 4 ⇒ 45 - 4 = 41 a = 9, b = 40 , c = 41 Semi perimeter(s) = 90/2 = 45 Area of triangle = √{45 (45 - 9) (45 - 41) (45 - 40)} = √{45 × 36 × 4 × 5} = √{3 × 3 × 5 × 6 × 6 × 2 × 2 × 5} = 3 × 5 × 6 × 2 = 180 cm2 |