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:

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