The floor of a hall has an area of 48 dm. The floor is to be tiled by triangular tiles. of sides 20 cm, 30 cm and 40 cm. Find the total cost of tiles if cost of each tile is Rs. 200.

The triangle is an obtuse triangle. No sides are equal.

convert cm to dm

1 dm = 10 cm

side a: 20 cm ⇒ 20cm * 1dm/10cm = 20dm/10 = 2 dm

side b: 30 cm ⇒ 30cm * 1dm/10cm = 30dm/10 = 3 dm

side c: 40 cm ⇒ 40cm * 1dm/10cm = 40dm/10 = 4 dm

We need to get the area of a triangle, but first we need to solve for its height using Heron's formula

s = (a+b+c) / 2 = (2+3+4) / 2 = 9/2 = 4.5

Area = √ (s (s-a) (s-b) (s-c)

h3/2 = √4.5 (4.5-2) (4.5-3) (4.5-4)

h3/2 = √4.5 (2.5) (1.5) (0.5)

h3/2 = √8.44

h3/2 = 2.91

h = (2.91*2) / 3

h = 1.94

A = hb/2 = (1.94*3) / 2 = 5.82/2 = 2.91 dm²

48 dm² / 2.91dm² = 16.5 or 17 tiles needed

17 x Rs200 = Rs3,400 is the total cost