Question

a floral design on a floor is made up of 16 tiles which are triangular the sides of the triangle being 9cm, 28 cm and 35 cm. find the cost of polishing the tiles at the rate of 50p per cm.​

Answer 1

$\\\large{\underline{\underline{\sf{\tt{Appropriate \: Question:}}}}}$

A floral 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. Find the cost of polishing the tiles at the rate of 50p per cm^2

$\\\large{\underline{\underline{\sf{\tt{Required \: Answer}}}}}$

$\\ \underline{\underline{\sf{\tt{Given}}}}$

$\\\sf{\rightarrow{A \: floral \: design \: on \: a \: floor \: made \: up \: of \: 16 \: tiles}}$

$\sf{\rightarrow{The \: dimensions \: of \: the \: rectangular \: tiles \: are \: 9cm ,\: 28cm ,\: and 35cm }}$

$\\ \underline{\underline{\sf{\tt{To \: Find:}}}}$

$\\ \sf{\rightarrow{The \: cost \: of \: polishing \: the \: tiles \: at \: 50p \: per \: {cm}^{2}}}$

$\\ \underline{\underline{\sf{\tt{Solution}}}}$

First, we have to find the area of the triangle shaped tiles.

Now,

$\sf{Semi-perimeter \: of \: 1 \: tile = \dfrac{9 + 28 + 35}{2}cm = \dfrac{72}{2} cm = \bold{36cm}}$

We know that:-

Heron's formula of area of a triangle :-

$\\ \underline{\boxed{\rm{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)}}}}$

Where,

• s is semi-perimeter
• a , b, c are the sides of the triangle.

Substituting the values of the sides:-

$\\ \bold{Area \: of \: the \: tile = \sqrt{36(36 - 9)(36 - 28)(36 - 35)} {cm}^{2} }$

$\\ \sf{\implies{\bold{Area \: of \: the \: tile } = \sqrt{36 \times 27 \times 8 \times 1}} {cm}^{2} }$

$\\ \sf{\implies{\bold{Area \: of \: the \: tile } = \sqrt{7776}} {cm}^{2} }$

$\\ \sf{\implies{\bold{Area \: of \: the \: tile } = \bold{88.2 {cm}^{2}}}} \: \: (approx)$

Therefore,

$\\\rm{Area \: of \: 16 \: tiles = 88.2 \times 16 {cm}^{2} = \bold{1411.2 {cm}^{2}}}$

We were given:-

$\\ \rm{Polishing \: 1 {cm}^{2} \: area \: of \: tiles \: costs \: 50p}$

$\rm{\rightarrow{Polishing \: 1411.2 {cm}^{2} \: area \: of \: tiles \: costs = (50 \times 1411.2)p}}$

$\rm{\therefore{Polishing \: 1411.2 {cm}^{2} \: area \: of \: tiles \: costs = 70560p = \red{\bold{Rs. 705.60}}}}$

$\\ \underline{\boxed{ \rm{Cost \: of \: polishing \: of \: the \: floral \: tiles \: is \:\green{\bold{Rs. 705.60\checkmark{}}}}}}$

Answer 2

Answer:

Step-by-step  

First, we have to find the area of the triangle shaped tiles.

Now,

We know that:-

Heron's formula of area of a triangle :-

Where,

s is semi-perimeter

a , b, c are the sides of the triangle.

Substituting the values of the sides:-

Therefore,

We were given:-

explanation: