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

Correct 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 4 tiles at the rate of ₹√14 per cm²

Given:

Dimensions of Triangle are:

• 12 cm
• 20 cm
• 24 cm

To find:

⟶ Area of Triangle

⟶ Cost of 4 tiles

Method:

$\sf{Applying \: Heron's \: formula,}\\\\\\\sf{s = \dfrac{a+b+c}{2}}\\\\\\\Rightarrow \sf{s = \dfrac{12+20+24}{2}}\\\\\\\implies \sf{s = \dfrac{56 }{2}}\\\\\implies \sf{s = 28 \: cm}$

$\bf{Area \: of \: triangle = \sqrt{s(s-a)(s-b)(s-c)} }\\\\\\\Rightarrow \sf{Area = \sqrt{28(28-12)(28-20)(28-24)} }\\\\\\\implies \sf{Area = 28 \times 16 \times 8 \times 4}\\\\\\\implies \sf{Area = \sqrt{14336} }\\\\\\\implies \boxed{\bf{Area = 119.73\: cm^{2} }}$

Area of 1 tile = 119.73 cm²

Area of  4 tiles = 4 × 119.73

∴ Area of 4 tiles = 478.92 cm²

Cost of each tile per cm² = ₹√14

Cost of 4 tiles of area 478.92 cm² = 478.92 × √14

Cost of 4 tiles of area 478.92 cm² = ₹1791.95

∴ Cost of 4 tiles = ₹1791.95