Question

a floor tile has the shape of a right angle triangle whose hypotenuse is 10 cm and one of the sides is 6 cm . how many such tiles are required to cover a floor of area 1298 m2.

Answer 1

$Hey\:!!..$

The answer goes here....

_______________________________________

》To find -

How many tiles are required to cover a floor of area $1298\:{m}^{2}$ ?

》Given -

Hypotenuse = $10\:cm$

Side = $6\:cm$

》Solution -

Since, the hypotenuse and side of the triangle is given.

Therefore, base -

⇒ $\sqrt{{10}^{2}-{6}^{2}}$

⇒ $\sqrt{100-36}$

⇒ $\sqrt{64}$

⇒ $8\:cm$

Using Herons formula -

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

Here, we have -

$a$ = $10\:cm$

$b$ = $6\:cm$

$c$ = $8\:cm$

$s$ = $\frac{a+b+c}{2}$ = $\frac{10+6+8}{2}$ = $12\:cm$

So, the area of the triangle -

⇒ $\sqrt{s(s-a)(s-b)(s-c)}$

⇒ $\sqrt{12(12-10)(12-6)(12-8)}$

⇒ $\sqrt{12(2)(6)(4)}$

⇒ $\sqrt{576}$

⇒ $24\:{cm}^{2}$

⇒ $0.0024\:{m}^{2}$

Now, the number of tiles whichis required to cover the floor -

⇒ $\frac{Area\:of\:floor}{Area\:of\:triangle}$

⇒ $\frac{1298}{0.0024}$

⇒ $540833.33$

Rounding it off we get -

⇒ $540833$

So, the number of tiles which is required to cover the floor is 540833 .

_______________________________________

Thanks !!..

Answer 2

HIIII BUDDY!!!!

As we are given that the triangle is a right angled triangle.

BY PYTHAGORAS THEOREM,

$h {}^{2} = p {}^{2} + b {}^{2}$

Substituting the values of hypothenuse and perpendicular, we get:-

$10 {}^{2} = 6 {}^{2} + b {}^{2}$

$100 = 36 + b^{2}$

$100 - 36 = b {}^{2}$

$64 = b {}^{2}$

$b = 8 \: cm$

THEREFORE, Base=8cm

Area of triangle=
$1 \div 2 \times 8 \times 6$

=$24 \: {cm}^{2}$

=$0.0024 {m}^{2}$

Tiles required=Area of floor/Area of triangle

=1298/0.0024

=540833.33

=540834 tiles.

THANKS

I THINK IT HELPS....

@Garu1678