Question

a floor design is made on a floor of a room by joining 4 triangular tiles of dimensions 12cm, 20cm and 24 cm each. Find the cost of the four tiles at the rate of Rs √14 per cm^2.​​

Answer 1

Given :

• A floor design is made on a floor of a room by joining 4 triangular tiles of dimensions 12cm, 20cm and 24 cm each.

To Find :

• The cost of the four tiles at the rate of Rs √14 per cm² = ?

Solution :

★ First of all we need to find the semi perimeter of traingle :

Let the sides of ∆ be as a = 12 , b = 20 cm and c = 24 cm.

➺ Semi Perimeter (s) = Sum of all sides of ∆ ÷ 2

➺ Semi Perimeter (s) = a + b + c ÷ 2

➺ Semi Perimeter (s) = (12 + 20 + 24) ÷ 2

➺ Semi Perimeter (s) = 56 ÷ 2

➺ Semi Perimeter (s) = 28 cm

• Hence,the semi perimeter of traingle is 28 cm.

★ Now,let's find the area of triangle by using herons formula :

➻ Area of ∆ = √s(s - a) (s - b) (s - c)

➻ Area of ∆ = √28(28 - 12) (28 - 20) (28 - 24)

➻ Area of ∆ = √28 × 16 × 8 × 4

➻ Area of ∆ = √14,336

➻ Area of ∆ = 119.7 cm²

• Hence,the area of ∆ is 119.7 cm².

★ Finding the area of 4 triangular tiles :

➝ Area of 4 triangular tiles = 4 × Area of ∆

➝ Area of 4 triangular tiles = 4 × 119.7

➝ Area of 4 triangular tiles = 478.8 cm²

• Hence,the area of 4 triangular tiles is 478.8 cm² .

★ Finding the cost of the four tiles at the rate of Rs √14 per cm² :

→ Cost of 4 tiles = √14 × area of 4 triangular tiles

→ Cost of 4 tiles = √14 × 478.8

→ Cost of 4 tiles = 3.74 × 478.8

→ Cost of 4 tiles = Rs. 1790.712

• Hence,the cost of 4 tiles is Rs.1790.712 .

Answer 2

Question :

A floor design is made on a floor of a room by joining 4 triangular tiles of dimensions 12 cm, 20 cm and 24 cm each. Find the cost of the four tiles at the rate of Rs √14 per cm²

Answer :

Given that :

• A floor design is made on a floor of a room by joining 4 triangular tiles of dimensions 12 cm, 20 cm and 24 cm each.

To find :

• The cost of the four tiles at the rate of Rs √14 per cm².

Solution :

• The cost of the four tiles at the rate of Rs √14 per cm² = Rupees 1790.712

Assuming the names of sides of triangle {Given}

• X = 12 cm
• Y = 20 cm
• Y = 24 cm

Using concept :

• Semi-perimeter of triangle.

• Area of triangle by using heron's formula.

• Area of 4 triangular tiles

• The cost of the four tiles (atq)

Using formula :

• Semi-perimeter of triangle = Sum of all sides of the triangle / 2

• Area of triangle by using heron's formula = √s(s-a)(s-b)(s-c)

• Area of 4 triangular tiles = 4 × A of ∆

• The cost of the four tiles (atq) = √14 × A of 4 triangular tile

What does the question say ?

• This question says that there is a floor design is made on a floor of a room by joining 4 triangular tiles of dimensions 12 cm, 20 cm and 24 cm each. Afterthat it ask us to find the cost of the four tiles at the rate of Rs √14 per cm².

Let's see the procedure now :

• To solve this problem we have to find the semi-perimeter of the given triangle by using this formula = Sum of all sides of the triangle / 2 putting the values we get 28 cm as semi-perimeter of ∆. Now using heron's formula of area of ∆ we have to using this formula = √s(s-a)(s-b)(s-c). We have to put the values and we get 119.7 cm² as the area of ∆. Afterwards finding area of 4 triangular tiles using the formula = 4 × A of ∆. And we get 478.8 cm² Now, finding the cost of the four tiles at the rate of Rs √14 per cm². Using formula = √14 × A of 4 triangular tile we get Rupees 1790.712 ac our final result.

Full solution :

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Finding semi-perimeter we get the following results.

↝ Semi-perimeter of triangle = Sum of all sides of the triangle / 2

↝ Semi-perimeter of triangle = (X + Y + Z) / 2

↝ Semi-perimeter of triangle = (12 cm + 20 cm + 24 cm) / 2

↝ Semi-perimeter of triangle = (32 cm + 24 cm) / 2

↝ Semi-perimeter of triangle = 56/2

↝ Semi-perimeter of triangle = 28 cm

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Now finding area of triangle by using heron's formula

↝ Area of triangle by using heron's formula = √s(s-a)(s-b)(s-c)

↝ Area of triangle by using heron's formula = √28(28-12)(28-20)(28-24)

↝ Area of triangle by using heron's formula = √28(16)(8)(4)

↝ Area of triangle by using heron's formula = √28 × 16 × 8 × 4

↝ Area of triangle by using heron's formula = √14336

↝ Area of triangle by using heron's formula = 119.7 cm²

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Now, finding the area of 4 triangular tiles

↝ Area of 4 triangular tiles = 4 × A of ∆

↝ Area of 4 triangular tiles = 4 × 119.7

↝ Area of 4 triangular tiles = 478.8 cm²

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Now finding the cost of the four tiles at the rate of Rs √14 per cm².

↝ The cost of the four tiles (atq) = √14 × A of 4 triangular tile

↝ The cost of the four tiles (atq) = √14 × 478.8

↝ The cost of the four tiles (atq) = 3.74 × 478.8

↝ The cost of the four tiles (atq) = 1790.712 Rupees.

Hence, the answer is 1790.712 Rupees.

The cost of the four tiles at the rate of Rs √14 per cm² = 1790.712 Rupees.