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 -

• Dimensions of Triangle 12 cm × 20 cm × 24 cm

To find -

• Area of Triangle

• Cost of 4 tiles

Solution -

First we will find the semi-perimeter

Semi-perimeter = $\sf\dfrac{a + b + c}{2}$

Semi-perimeter = $\sf\dfrac{12 + 20 + 24}{2}$

Semi-perimeter =$\cancel{\dfrac{56}{2}}$

Semi-perimeter = $28$

Now,

Using heron's formula -

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

$\sf \sqrt{28(28 - 12)(28 - 20)(28 - 24)}$

$\sf \sqrt{28 \times 16 \times 8 \times 4}$

$\sf 119.73 \: cm^{2}$

Now,

Area of 1 tile = 119.73 cm²

Area of 4 tiles = 4 × 119.73

∴ Area of 4 tiles = 478.92 cm²

Now,

Cost of each tile per cm² = ₹√14

Cost of 4 tiles = 478.92 × √14

Cost of 4 tiles = ₹1791.95

∴ Cost of 4 tiles = ₹1791.95

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Answer 2

Answer:

Step-by-step explanation:

Given,

Dimensions are 12cm,20cm and 24cm.

To Find,

Cost of the four tiles at the rate of Rs √14 per cm².​​

Formula to be used,

Heron's formula,

Area of triangle = √S(S - A) × (S - B) × (S - C)

Solution,

S = (A + B + C)/2

S = (12 + 20 + 24)/2

S = 56/2 = 28 cm

So, putting on the formula, we get

Area of triangle = √S(S - A) × (S - B) × (S - C)

⇒ Area of triangle = √[28(28 - 12) × (28 - 20) × (28 - 24)]

⇒ Area of triangle = √[28 × 16 × 8 × 4]

⇒ Area of triangle = 14436

⇒ Area of triangle = 119.73 cm²

Here, the Area of the triangle is 119.73 cm².

Now, the cost of 4 triangular tiles,

= 4 × 119.73 = 478.92 cm².

Now,  the cost of four tiles,

= 478.92 × √14  = Rs 1791.95

Hence, the cost of 4 tiles is Rs 1791.95.