Question

13. A design on a wall is made up of 20 tiles which are triangular, the sides of
the triangle being 13cm, 14cm, and 15cm. Find the cost of polishing the tiles at
the rate of 25p per square cm.​

Answer 1

Answer:

Cost of polishing = Rs.420

Step-by-step explanation:

Given:

• Number of tiles = 20
• Sides of the triangle = 13 cm, 14 cm, 15 cm
• Rate of polishing = 25 p per cm²

To Find:

• The total cost of polishing the tiles

Solution:

Here we have to first find the total surface area of one tile.

By Heron's formula,

$\sf Area\:of\:a\:triangle=\sqrt{s(s-a)(s-b)(s-c)}$

where s is the semi perimeter of the triangle

a, b, c are the length of each of the three sides,

Here semi perimeter is given by,

s = (13 + 14 + 15)/2

s = 42/2 = 21 cm

Substituting the datas we get,

$\sf Area\:of\:the\:triangle=\sqrt{21(21-13)(21-14)(21-15)}$

$\sf \implies \sqrt{21\times 8\times 7\times 6}$

$\sf \implies \sqrt{7056}$

$\sf \implies 84\:cm^{2}$

Hence the area of each tile is 84 cm²

Now,

Area of 20 tiles = Area of 1 tile × 20

Area of 20 tiles = 84 × 20

Area of 20 tiles = 1680 cm²

Hence the total surface area of all the tiles is 1680 cm².

Now finding the total rate of polishing,

Total cost of polishing = Area to polish × Rate per cm²

Total cost of polishing = 1680 × 25

Total cost of polishing = 42000 p = Rs. 420

Hence the total cost of polishing is 420 rupees.

Answer 2

Question

A design on a wall is made up of 20 tiles which are triangular, the sides of the triangle being 13cm, 14cm, and 15cm. Find the cost of polishing the tiles at the rate of 25p per square cm.

Solution

Sides of the triangle = 13cm, 14cm and 15cm

By using Heron's Formula

$\frac{a + b + c}{2} = \frac{13 + 14 + 15}{2} = \frac{42}{2} = 21 \\ \\ area \: = \sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{21(21 - 13)(21 - 14)(21 - 15)} \\ = \sqrt{21 \times 8 \times 7 \times 6} \\ = \sqrt{7056} = 84$

We have found only the area of one triangle

Area of 20 triangles = (84×20)cm² = 1680cm²

Cost of polishing the tiles at the rate of 25p per cm² = (1680×25)p = 42000p

Now we have to convert 42000p into rupees

= ₹(42000/100)

= ₹420

Ans:- The cost of polishing the tiles at the rate of 25p per square cm is ₹420.

More Information

Surface area of cuboid = 2(lb+bh+lh)

Surface area of cube = 6(side)²

Area of four walls = 2(l+b)h

Lateral surface area of cuboid = 2(l+b)h

Lateral surface area of cube = 4(side)²