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 (see Fig. 12.18). Find the cost of polishing the tiles at the rate of 50p per cm2.
Solution:
Given: Dimensions of the triangular tiles.
By using Heron’s formula, we can calculate the area of triangle.
Heron's formula for the area of a triangle, Area = √s(s - a)(s - b)(s - c)
Where a, b and c are the sides of the triangle, and s = Semi-perimeter = Half the Perimeter of the triangle = (a + b + c)/2
We have the dimensions of sides of each triangular tile.
a = 35 cm, b = 28 cm, c = 9 cm
Semi Perimeter(s) = (a + b + c)/2
s = (35 + 28 + 9)/2
s = 72/2
s = 36 cm
By using Heron’s formula,
Area of each triangular tile = √s(s - a)(s - b)(s - c)
= √36(36 - 35)(36 - 28)(36 - 9)
= √36 × 1 × 8 × 27
= 36√6 cm2
Area of a 1 triangular tile = 36√6 cm2
Area of 16 triangular tile = 16 × 36√6 cm2
= 16 × 36 × 2.45 cm2
= 1411.2 cm2
Since, the cost of polishing 1cm2 of tiles is 50p or ₹ 0.5
Therefore, the cost of polishing 1411.2 cm2 area of tiles = 1411.2 cm2 × 0.5 = ₹ 705.60
☛ Check: NCERT Solutions Class 9 Maths Chapter 12
Video Solution:
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 (see Fig. 12.18). Find the cost of polishing the tiles at the rate of 50p per cm².
Class 9 Maths NCERT Solutions Chapter 12 Exercise 12.2 Question 8
Summary:
It is given that there is a floral design on a floor that is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm, and 35 cm. We have found that the cost of polishing all the tiles at the rate of 50p per cm2 is ₹ 705.60.
☛ Related Questions:
- Radha made a picture of an aeroplane with coloured paper as shown in Fig 12.15. Find the total area of the paper used.
- A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm, and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
- A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?
- An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (See Fig. 12.16), each piece measuring 20 cm, 50 cm, and 50 cm. How much cloth of each colour is required for the umbrella?