Question

A floor is made up of 20 triangular tiles, each with sides 40 cm, 24 cm and 32 cm. Find the cost of polishing the floor at the rate of 2 rupees per sq.cm.​

Answer 1

Answer:

$15360\,\,rupees$

Step-by-step explanation:

Let sides of the triangle be $a,b,c$

$a=40\,,\,b=24\,,\,c=32$

Semi-perimeter (s) = $\frac{a+b+c}{2}$

$=\frac{40+24+32}{2}\\ =\frac{96}{2}\\=48$

Area of one tile $=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{48(48-40)(48-24)(48-32)}\\ =\sqrt{48(8)(24)(16)}\\ =\sqrt{147456} \\=384\,\,cm^2$

So,

Area of 20 tiles $=20(384)=7680\,\,cm^2$

Cost of polishing the floor at the rate of 2 rupees per sq.cm = $7680(2)=15360\,\,rupees$