Question

This former Indian state is now divided among the states Andhra Pradesh, Karnataka and Maharashtra. Its name is also the name of a walled city, today capital of Andhra Pradesh. ​

Answer 1

Answer:

today's capital of Andhra Pradesh is Amaravati

Answer 2

Answer:

vggg

Explanation:

\large\underline{\sf{Solution-}}

Solution−

Dimensions of rectangular room

Length of room = 45 cm

Breadth of room = 25 cm

Now, it is given that rectangular room measuring 45 cm by 25 cm is to be tiled using square tiles.

So, edge of square tile = HCF (45, 25)

Calculations of HCF of 45 and 25

Prime factorization of 45 = 3 × 3 × 5

Prime factorization of 25 = 5 × 5

It implies, HCF (45, 25) = 5

So, it means, edge of square tile = 5 cm.

So, largest size of tile that can be used to tile the floor is 5 cm.

Let assume that n number of tiles are needed to tile the floor, without cutting.

\begin{gathered}\rm \: n \times Area_{(tile)} = Area_{(Room)} \\ \end{gathered}

n×Area

(tile)

=Area

(Room)

\begin{gathered}\rm \: n \times {(5)}^{2} = 45 \times 25 \\ \end{gathered}

n×(5)

2

=45×25

\begin{gathered}\rm \: n \times 25 = 45 \times 25 \\ \end{gathered}

n×25=45×25

\begin{gathered}\rm\implies \:n \: = \: 45 \\ \end{gathered}

⟹n=45

Hence, 45 number of tiles are needed to tile the floor, without cutting.

\rule{190pt}{2pt}

Formulae Used :-

\begin{gathered}\boxed{ \rm{ \:Area_{(Rectangle)} = Length \times breadth \: }} \\ \end{gathered}

Area

(Rectangle)

=Length×breadth

\begin{gathered}\boxed{ \rm{ \:Area_{(Square)} = {(side)}^{2} \: }} \\ \end{gathered}

Area

(Square)

=(side)

2

\rule{190pt}{2pt}

Additional information :-

\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}\end{gathered}

†

FormulasofAreas:−

⋆Square=(side)

2

⋆Rectangle=Length×Breadth

⋆Triangle=

2

1

×Base×Height

⋆Scalene△=

s(s−a)(s−b)(s−c)

⋆Rhombus=

2

1

×d

1

×d

2

⋆Rhombus=

2

1

d

4a

2

−d

2

⋆Parallelogram=Base×Height

⋆Trapezium=

2

1

(a+b)×Height

⋆EquilateralTriangle=

4

3

(side)

2