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 rate of 50 paise per cm square ​

Answer 1

Step-by-step explanation:

Solution:

Semi-perimeter of 1 triangular tile  

=s

=(9+28+35)/2=72/2=36 cm

Using Heron's formula, Area of 1 triangular tile  

=√{s(s−9)(s−28)(s−35)}

=√{36(36−9)(36−28)(36−35)}

=√{36×27×8×1}

=88.2 cm^2   (approx.)        

⇒ Area of 16 triangular tiles =16×88.2=1411.2 cm^2.

Polishing of 1 cm^2 of area costs 50 p

Polishing of 1411.2 cm^2 of area would cost =50×1411.2=70560p= Rs 705.60

hope, this will help you.

Answer 2

• Cost of polishing the tiles = Rs. 705.6.

Given :–

• A flora design on a floor is made up of 16 tiles which are triangular.
• The sides of the triangle = 9cm, 28cm and 35cm.

To Find :–

• The cost of polishing the tiles at rate of 50 paise per cm².

Solution :–

First we need to find the area of the traingle.

by heron's formula,

$\hookrightarrow \sqrt{s(s - a)(s - b)(s - c)}$

Where,

$\hookrightarrow s = \dfrac{a + b + c}{2}$

We have,

• a = 9cm.
• b = 28cm.
• c = 35cm.

$\hookrightarrow s = \dfrac{9 + 28 + 35}{2} \: cm$

$\hookrightarrow s = \cancel \dfrac{72}{2} \: cm$

$\hookrightarrow \: s = 36 \: cm$

Now,

Substitute all the values in the heron's formula,

$\hookrightarrow\sqrt{36(36 - 9)(36 - 28)(36 - 35)} \: {cm}^{2}$

$\hookrightarrow \sqrt{36(27)(8)(1)} \: {cm}^{2}$

$\hookrightarrow\sqrt{(6 \times 6)(3 \times 3 \times 3)( 2 \times 2 \times 2)} \: {cm}^{2}$

$\hookrightarrow \sqrt{ {(6)}^{2} \times {(3)}^{2} \times {(2)}^{2} \times (2 \times 3) } \: {cm}^{2}$

$\hookrightarrow 6 \times 3 \times 2 \sqrt{6} \: {cm}^{2}$

$\hookrightarrow 6 \times 6 \sqrt{ 6 } \: {cm}^{2}$

$\hookrightarrow 36 \sqrt{6} \: {cm}^{2}$

We know that,

• √6 = 2.45

$\hookrightarrow 36 \times 2.45 \: {cm}^{2}$

$\hookrightarrow 88.2 \: {cm}^{2}$

Now, we need to find the area of the tiles.

In the given question,

Total tiles = 16.

Area of tiles = 16 × Area of a triangle

We have,

• Area of a triangle = 88.2 cm²

$\hookrightarrow 16 \times 88.2 \: {cm}^{2}$

$\hookrightarrow 1411.2 \: {cm}^{2}$

Now, we have to find the cost of polishing the tiles.

Given,

Cost of polishing the tiles = 50 paise per cm²

We know that,

• 50 paise = $Rs. \: \sf \dfrac {1}{2}$

For 1411.2 cm²,

$\hookrightarrow1411.2 \: \times \dfrac{1}{2}$

$\hookrightarrow\dfrac{ \cancel{14112}}{10} \times \dfrac{1}{ \cancel2}$

$\hookrightarrow\dfrac{7056}{10}$

$\hookrightarrow705.6$

Hence,

The cost of polishing the tiles is Rs. 705.6.