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.​


Kindly don't spam ​

Answer 1

$\red{\:❥ᴀɴsᴡᴇʀ}$

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

$</p><p>Semi-perimeter = \sf\dfrac{a + b + c}{2} </p><p>$

2a+b+c

$semi \: -perimeter = \sf\dfrac{12 + 20 + 24}{2} </p><p>212+20+24$

$</p><p>Semi-perimeter =\cancel{\dfrac{56}{2}} </p><p>256$

Semi-perimeter = 28 28

Now,

Using heron's formula -

$</p><p>\sf \sqrt{s(s - a)(s - b)(s - c)} </p><p>s(s−a)(s−b)(s−c)$

$</p><p>\sf \sqrt{28(28 - 12)(28 - 20)(28 - 24)} </p><p>28(28−12)(28−20)(28−24)</p><p>$

$</p><p>\sf \sqrt{28 \times 16 \times 8 \times 4} </p><p>28×16×8×4$

$\sf 119.73 \: cm^{2} 119.73cm </p><p>2</p><p>$

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

I hope it is helpful for you

@ Aman jha