Question

A floral design on a floor is made up of 16 tiles which are triangular. The sides of the triangular tiles are 26 cm, 20 cm and 10 cm. The tiles are polished at the rate of 20 paise per $c{m}^2.$ Find the cost of polishing the tiles.

• A.
  Rs 287.23
• B.
  Rs 276
• C.
  Rs 299
  
• D.
  None of these

Answer 1

The correct option is A

Rs 287.23

In one triangular tiles,
$s=\frac{20+10+26}{2}=28cm$

Area of one triangular tile
$=\sqrt{s(s-10)(s-20)(s-26)}=\sqrt{28\times (28-10)(28-20)(28-26)}=\sqrt{28\times 18\times 8\times 2}=\sqrt{2\times 2\times 7\times 2\times 3\times 3\times 2\times 2\times 2\times 2}=\sqrt{2^2\times 3^2\times 2^2\times 2^2\times 14}=2\times 3\times 2\times 2\times \sqrt{14}=24\sqrt{4}c{m}^2=24\times 3.74=89.761c{m}^2$

Area of floral dsign

$=16\times areaofonetriangulartile=16\times 89.761=1436.16c{m}^2$

The required cost of polishing the given design
= ₹ $\frac{20}{100}\times 1436.16$

= ₹ $287.23$