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:
Answer & explanation
Correct answer: option 3
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