Question

A foral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being $9$ cm, $28$ cm and $35$ cm (See Fig.). Find the cost of polishing the tiles at the rate of $50$ p per $c{m}^2$.

• A. $Rs705.6$
• B. $Rs735.6$
  
• C. $Rs605.6$
  
• D. $Rs905.6$
  

Answer 1

The correct option is A $Rs705.6$

Number of tiles$=16$

Area of $16$ tiles$=16\times$ area of $1$ triangular tile

$\therefore$ Area of $1$ triangular tile$=\sqrt{s(s-a)(s-b)(s-c)}$

$s=\frac{a+b+c}{2}=\frac{35+9+28}{2}=36㎝$

Area of $1$ tile$=\sqrt{36(36-35)(36-9)(36-28)}$

$=\sqrt{36\times 1\times 27\times 8}=\sqrt{9\times 4\times 1\times 9\times 3\times 2\times 2\times 2}$

$=2\times 2\times 9\sqrt{6}=36\sqrt{6}㎝$

$=36\times 2.45=88.2㎠$

Area of $16$ tiles$=16\times 88.2=1411.2㎠$

Cost of polishing$1411.2㎠=(0.5\times 1411.2)=$Rs.$705.60$