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 50 paise per cm2

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Answer 1

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We have lengths of the sides of 1 triangular tile are a = 35 cm, b = 28 cm, c = 9 cm. 
∴ s = a +b + c/ 2 = 35 + 28 +9 /2 cm = 36 cm 

AREA OF FIRST TRIANGULAR TILE =

$\sqrt{s(s - a)(s - b)(s - c)}$
=
$\sqrt{36(36 - 35)(36 - 28)(36 - 9)} cm {?}^{2}$

=
$\sqrt{36 \times 1 \times 8 \times 27cm ^{2} }$
=
$\sqrt{7776 \: cm {}^{2} }$
=88.2cm^2

Cost of polishing 1 cm2 = 50 p = Re 0.50 
∴ Total cost of polishing the floral design = Rs 16 ×

88.2 × 0.50 

= Rs 705.60 Ans.

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Answer 2

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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.

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