Question

A floral design of a floor is made up of 16 tiles which are triangular. The side of the triangle being 9 cm, 28 cm, and 35 cm. Find the cost of polishing the tiles, at rs 50 paisa/sq cm.

Answer 1

$\huge\bf{\underline{\red{SOLUTION:-}}}$

$\sf\bullet Sides\:of\: \triangle=9cm\:,28cm\:and\:35cm\\ \\ \sf\bullet Cost\:of\: polishing=50paisa/cm{}^{2}$

Now

• Find the Area of 1 tile by Heron's formula

$\boxed{\sf{\dag{\:\:Area\:of\triangle=\sqrt{s(s-a)(s-b)(s-c)}}}}\\ \\ \sf\leadsto s=\dfrac{a+b+c}{2}\\ \\ \sf\implies s= \dfrac{9+28+35}{2}\\ \\ \sf\implies s=\cancel{\dfrac{72}{2}}\\ \\ \sf\implies {\green{semi\: perimeter=36}}$

• Now the Area of 1 tile

$\sf:\implies Area=\sqrt{36(36-9)(36-28)(36-35)}\\ \\ \sf\implies Area=\sqrt{36\times 27\times 8\times 1}\\ \\ \sf:\implies Area=\sqrt{6\times 6\times 3\times 3\times 3\times 2\times 2\times 2}\\ \\ \sf:\implies Area=6\times 3\times 2\sqrt{6}cm{}^{2}\\ \\ \sf\implies Area= 36\sqrt{6}cm{}^{2}\\ \\ \sf\bullet \:\:\: \sqrt{6}=2.45\\ \\ \sf:\implies Area= 36\times 2.45\\ \\ \sf:\implies Area\:of\: triangle=88.2cm{}^{2}$

$\sf\bullet {\purple{Now\:the\:Area\:of\:16\: triangular\:tiles}}\\ \\ \sf\implies 88.2\times 16\\ \\ \sf\implies 1411.2cm{}^{2}$

$\sf\bullet {\blue{Cost\:of\: polishing=50paise/cm{}^{2}}}\\ \\ \sf\implies 50\times 1411.5\\ \\ \sf\implies 70560\:Paise\\ \\ \sf or\:\:\:\dfrac{70560}{100}Rs\:\:= 705.6rs$

$\boxed{\sf{Cost\:of\: polishing=70560Paise\:\:or\:705.6Rs}}$

Answer 2

Answer:

$\large{\underline{\boxed{\mathfrak\blue{Cost \: of \: polishing = Rs.705 \: \: \: [Approx.] }}}}$

Given:-

• Sides if triangle = 9 cm, 28 cm, 35 cm
• Number of tiles = 16
• Rate of polishing = 50 paisa/sq.cm

To find:-

• Cost of polishing = ?

As the sides of triangle are given,

$\sf So, semi - perimeter(s) = \dfrac{perimeter}{2} \\\\\dashrightarrow\sf s = \dfrac{9 + 28 + 35}{2} \\\\\dashrightarrow\sf s = \dfrac{72}{2} \\\\\dashrightarrow\sf s = {\boxed{\sf\green{36 \: cm }}}$

$\sf We \:know, \\\\\star \: {\boxed{\rm{Area_{\triangle} = \sqrt{s(s - a)(s - b)(s - c)} }}}$

$\dashrightarrow\sf Area = \sqrt{36(36 - 9)(36 - 28)(36 - 35)} \\\\\dashrightarrow\sf Area = \sqrt{36 \times 27 \times 8 \times 1} \\\\\dashrightarrow\sf Area = \sqrt{7776} \\\\\dashrightarrow\sf Area ={\boxed{\sf\purple{ 88.18 \: cm^2 \: \: \: [Approx.] }}}$

Total tiles = 16

$\sf So,total \: area = (88.18 \times 16)\:cm^2 \\\\\dashrightarrow\sf Total \: area ={\boxed{\sf\blue{ 1410.88 \: cm^2 \: \: \: [Approx.]}}}$

$\rule{200}{1}$

$\sf Rate = 50 \: paisa/cm^2 \\\\\dashrightarrow\sf Rate = Rs.0.5/cm^2$

$\sf Cost \: of \: polishing = Area \times Rate \\\\\dashrightarrow\sf Cost \: of \: polishing = Rs.(1410.88 \times 0.5) \\\\\dashrightarrow\sf Cost \: of \:polishing =Rs. 705.44 \\\\\dashrightarrow\large{\boxed{\sf\green{ Cost \: of \: polishing \approx Rs.705 \: \: \: }}}$