Question

A floral design on a floor on a floor is made up of 16 tiles which are triangular, the sides of the triangular being 9cm,28cm and 35cm.Find the of a polishing the tiles at the rate of 50p per cm².​

Answer 1

Answer:

Given that,

______________

A = 9 cm

b = 28 cm

c = 35 cm

Therefore,

$s = \frac{a + b + c}{2}$

$= \frac{9 + 28 + 35}{2}$

$= \frac{72}{2}$

$= 36 \: cm$

Area of the triangular tile is

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

$= \sqrt{36(36 - 9)(36 - 28)(36 - 35)}$

$= \sqrt{36 \times 27 \times 8}$

$= \sqrt{36 \times 9 \times 3 \times 4 \times 2}$

$= 6 \times 3 \times 2 \times \sqrt{3 \times 2}$

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

$=( 36 \sqrt{6} \times 2.45)c {m}^{2}$

$= 88.2 \: c {m}^{2}$

Therefore, the total area of the tile is = 16 × 88.2 cm²

= 1411.2 cm²

Hence, The cost of polishing per cm² area = 50p

Than, Total cost of polishing the tiles = 50p×1411.2 cm²

= Rs. 705.60

Therefore, It cost Rs. 705.60 while polishing the complete tiles.

Answer 2

$\huge\bigstar\underline\mathfrak\orange{Answer:-}$

$\large\sf\green{Given:-}$

$\sf{a\:=\:9cm}$

$\sf{b\:=\:28cm}$

$\sf{c\:=\:35cm}$

$\large\sf\pink{Formula:-}$

$\longrightarrow$$\sf{s}$ = $\sf\frac{a+b+c}{2}$

$\longrightarrow$$\sf{s}$ = $\sf\frac{9+28+35}{2}$

$\longrightarrow$$\sf{s}$ = $\sf\frac{72}{2}$

$\longrightarrow$$\sf{36cm}$

$\large\sf\red{Area\:of\:triangular\:tile\:is}$

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

$\longrightarrow$$\sf\sqrt{36(36 - 9)(36 - 28)(36 - 35)}$

$\longrightarrow$$\sf\sqrt{36 - 27 - 8}$

$\longrightarrow$$\sf\sqrt{36 \times 9 \times 3 \times 4 \times 2}$

$\longrightarrow$$\sf6 \times 3 \times 2 \times \sqrt{3 \times 2}$

$\longrightarrow$$\sf36 { \sqrt{6cm} }^{2}$

$\longrightarrow$$\sf(36 \sqrt{6} \times 2.42) {cm}^{2}$

$\longrightarrow$$\sf{88.2cm}^{2}$

$\sf\green{Therefore,\:the\:total\:area\:of\:the\:tile\:is\:</p><p>=\:16\:×\: 88.2 cm²}$

$\sf{=\:1411.2\:cm²}$

$\sf\red{Hence,\:The\:cost\:of\:polishing\:per\:cm²\:are\:=\:</p><p>50p}$

$\sf\pink{Than,\:Total\:cost\:of\:polishing\:the\:tiles\:=</p><p>\50p×1411.2 cm²}$

$\longrightarrow$$\sf{=\:Rs.705.60}$

$\sf\orange{Therefore,\:It\:cost\:Rs.\:</p><p> 705.60\:while\:polishing\:the\:complete\:</p><p> tiles}$