Question

A floral design on a floor is made up of $16$ tiles which are triangular. The sides of the triangular tile are $26cm,20cm$ and $10cm$. The tiles are polished at the rate of $20$ paise per $c{m}^2$, then the cost of polishing the tiles is Rs. $584.25$. (Take $\sqrt{14}=3.74)$

• A. True
• B. False

Answer 1

The correct option is B False

Given, in one triangular tile, we have $a=26cm,b=20cm,c=10cm$
$Semi-perimeter,s=\frac{a+b+c}{2}=\frac{26cm+20cm+10cm}{2}=28cm$
Area of the triangular tile $=\sqrt{28\times (28-26)\times (28-20)\times (28-10)}$
$=\sqrt{28\times 2\times 8\times 18}$

$=24\sqrt{14}{cm}^2$
So, area of 16 triangular tiles $=16\times$ Area of one triangular tile

$=16\times 24\sqrt{14}$

$=384\sqrt{14}{cm}^2$
Given, cost of polishing the tiles is $20$ paise per ${cm}^2$.
Therefore, cost of polishing $384\sqrt{14}{cm}^2=384\sqrt{14}\times 0.20$
$=384\times 3.74\times 0.20$

$=Rs.287.232$