Question

The length of hall exceeds its breadth by 12m.If the perimeter of hall is 76 m, find the cost of carpeting it at Rs4 per sq.m.

Answer 1

Answer:

$\huge\colorbox{Brown}{Answer ☝}$

Answer 2

${\huge{\boxed{\underline{\overline{\rm{Question:-}}}}}}$

Q) The length of a hall exceeds it's breadth by 12m . If the perimeter of the hall is 76m , find the cost of carpeting it at Rs 4 per sq. m.

${\huge{\underbrace{\rm{Answer\checkmark}}}}$

$\frak{Given}\begin{cases}\rm{The\:\bf{length}\:exceeds\:the\:\bf{breadth}\;by\;\bf{12m.}}\\ \rm{Rate\;of\;carpeting=\bf{Rs\:4\:per\:sq.m.}}\end{cases}$

${\large{\underline{\bf{\maltese\:To\:Find:-}}}}$

• The cost of carpeting at the rate of Rs 4 per sq. m.

$\large{\underline{\bf{\maltese\:Solution:-}}}$

${\textit{\textbf{Finding\:Length\:and\:Breadth}}}$

We know,

• Length = breadth + 12 m.

and

• Perimeter = 76 m.

So,

# Let breadth be x.

• Length = x + 12

$\sf \mapsto \: perimeter _{rectangle} = 2(length + breadth) \\ \\ \colon \sf\implies \: \cancel{ 76} \: m = \cancel 2 \{(x + 12) + x \} \\ \\ \colon \sf \implies \: 38 \: m = 2x + 12 \\ \\ \colon \sf \implies \: 2x = 38 - 12 \\ \\ \colon \sf \implies \: \cancel 2x = \cancel{ 26} \\ \\ \longrightarrow \boxed{ \bf{x = \pink{13 \: m}}}$

So,

$\mapsto \sf \: breadth = x \: m \\ \\ \leadsto \: \: \underline{ \boxed{ \bf{ breadth = \blue{13 \: m}}}}$

And

$\sf \mapsto \: length = x + 12 \: m \\ \\ \mapsto \sf \: length = 13 + 12 \: m \\ \\ \leadsto \: \underline{ \boxed{ \bf{length = \purple{25 \: m}}}}$

${\textit{\textbf{Finding\:the\:cost}}}$

As we are carpeting the floor so ,

we have to first find the area of the floor.

We have :

• Length = 25 m
• Breadth = 13 m

$\mapsto \sf \: area _{rectangle} = length \times breadth \\ \\ \colon \implies \sf \: area = 25 \times 13 \: {m}^{2} \\ \\ \colon \implies \boxed{ \bf{ area = \orange{325 \: {m}^{2} }}}$

Now ,

We know

• Rate of carpeting = Rs 4 per m²

And,

$\star \longrightarrow \sf \: cost = area \times rate \\ \\ \tt \: so \\ \\ \colon \implies \sf \: cost = 325 \times 4 \\ \\ \colon \implies \underline{ \boxed{ \bf{ \red{cost = 1300 \: rs}}}}$

★ Required Answer :

♦ Cost of carpeting the Hall = 1300 Rs .

_____________________________