Question

A floral design on a floor is made up of 16 tiles is triangular in shape having side of a triangle being 9 cm 28cm and 35 cm find the cost of polishing the tiles at the rate of 50p per cm

Answer 1

$\boxed{\bold{\large{Answer:}}}$

For one tile:

a = 9cm

b = 28cm

c = 35cm

$s = \frac{a + b + c}{2} = \frac{9 + 28 + 35}{2} \\ \\ = 36cm$

Area of one tile,

$\implies \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \implies \: \sqrt{36(36 - 9)(36 - 28)(36 - 35)} \\ \\ \implies \: \sqrt{36(27)(8)(1)} = \sqrt{36(9 \times 3)(4 \times 2)} \\ \\ \implies \: 6 \times 3 \times 2 \sqrt{6} = 36 \sqrt{6}c {m}^{2}$

∴ Area of 16 tiles

$= 36 \sqrt{6} \times 16 = 576 \sqrt{6} c {m}^{2}$

∴ Cost of polishing the tiles at the rate of 50 p per cm²

$\implies \: 576 \sqrt{6} \times 50p = \frac{576 \sqrt{6} \times 50}{100} \\ \\ \implies \: 288 \sqrt{6} = 705.60 \: rs$

$\boxed{\bold{\large{Hope\:it\:helps\:you!}}}$

Answer 2

Given,
sides of tri. 》》9 cm,28cm and 35 cm.
s=9+28+35/2=36 cm
Using heron's formula,
=_/s(s-a)(s-b)(s-c)
=_/36(36-9)(36-28)(36-35)
=_/36·27·8·1
=36_/6 cm^2.
Now for 16 tiles,
36_/6 · 16=576_/6 cm^2.
Now,for 50 p per cm,
=576_/6 ·50/100=705.60 rs.