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

Answer 1

Area of tiles = 16 x area of 1 Δ

S=

2

a+b+c

=

2

9+28+35

=

2

72

=36

Area=

36(36−9)(36−28)(36−35)

36×27×8×1

36

6

cm

2

Area of tiles = 16 ×36

6

=1410.20.

Cost of polishing per cm

2

= 50.

Cost of polishing = 1410.90 cm

2

1410.90 x

2

1

705.45

Answer 2

Answer:

$\sf\red{α = 9 cm,\: b = 28 cm, \:c = 35 cm}$

$\displaystyle{\sf{\pink \therefore s= \dfrac{a+b+c}{2} = \dfrac{9+28+35}{2}}}$

$\blue \implies{\sf\green{36\:cm}}$

$\purple \therefore$ Areα of one tile

$\displaystyle{\sf\orange{\red\implies \sqrt{s(s-a)(s-b)(s-c)}}}$

$\displaystyle{\sf\pink{\purple\implies \sqrt{36(36-9)(36-28)(36-35)}}}$

$\displaystyle{\sf\green{\blue \implies\sqrt{36(17)(8)(1)}}}$

$\displaystyle{\sf\red{\orange \implies 36\sqrt{6}cm^{2}}}$

$\red {\therefore}$Areα of 16 tile

$\displaystyle{\sf\blue{\green \implies36\sqrt{6}cm^{2}\times16 = 576\sqrt{6}cm^{2}}}$

$\orange \therefore \sf\red{Cost \:of\: polishing \:the\: tiles \:αt \:the\: rαte \:of \:50p \:percm²}$

$\pink \implies{\sf\purple{576 \sqrt{6} \times 50p = ₹ \dfrac{576 \sqrt{6} \times 60}{100}}}$

$\orange \implies{\sf\red{₹288 \sqrt{6}}}$

$\green\large{\implies{\boxed{\bf\blue{\blue{₹705.60}}}}}$