Question

The length and the breadth of a rectangle park area in the ratio 5:3 and it's perimeter is 128m Find the area of the park.

Answer 1

GIVEN:

• The length and the breadth of a rectangle park area in the ratio 5:3
• The perimeter of park is 128 m

TO FIND:

• What is the area of the rectangular park ?

SOLUTION:

Let 'x' be the common in given ratios

• LENGTH = 5x
• BREADTH = 3x

We know that the formula for finding the perimeter of rectangular park is:-

$\large{\boxed{\bf{\star \: PERIMETER = 2(L+B) \: \star}}}$

According to question:-

$\rm{\longrightarrow 128 = 2(5x +3x) }$

$\rm{\longrightarrow 128 = 2 \times 8x }$

$\rm{\longrightarrow 128 = 16x }$

$\rm{\longrightarrow \cancel\dfrac{128}{16} = x }$

$\large\bf{\star \: 8 = x \: \star}$

• LENGTH = 5x = 5(8) = 40 m
• BREADTH = 3x = 3(8) = 24 m

To find the area of the rectangular park, we use the formula:-

$\large{\boxed{\bf{\star \: AREA = LENGTH \times BREADTH \: \star}}}$

According to question:-

$\rm{\longrightarrow AREA = 40 \times 24 }$

$\large\bf{\star \: AREA = 960 \: m^2 \: \star}$

❝ Hence, the area of the rectangular park is 960 m² ❞

______________________

Answer 2

QUESTION:-

ᴛʜᴇ ʟᴇɴɢᴛʜ ᴀɴᴅ ᴛʜᴇ ʙʀᴇᴀᴅᴛʜ ᴏғ ᴀ ʀᴇᴄᴛᴀɴɢʟᴇ ᴘᴀʀᴋ ᴀʀᴇᴀ ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ 5:3 ᴀɴᴅ ɪᴛ's ᴘᴇʀɪᴍᴇᴛᴇʀ ɪs 128ᴍ ғɪɴᴅ ᴛʜᴇ ᴀʀᴇᴀ ᴏғ ᴛʜᴇ ᴘᴀʀᴋ.

ANSWER✓

$\Large\underline\bold{GIVEN}$

$\sf\dashrightarrow RATIO\:OF\:L:B =5:3$

$\sf\dashrightarrow perimeter\:of\:park(rectangle) =128m$

$\Large\underline\bold{TO\:FIND,}$

$\sf\large\dashrightarrow area\:of\:rectangle$

$\Large\underline\bold{SOLUTION,}$

$\sf\large\therefore NOW,$

$\sf\therefore let\:the\:length(L)\:be\:5x.........eq^1$

$\sf\therefore let\:the\:breadth(B)\:be\:3x.......eq^2$

$\Large\underline\bold{using\:formula,}$

$\sf\implies perimeter\:of\:rectangle= 2 \times (L+B)$

$\sf\implies area\:of\:rectangle= Length \times Breadth$

A.T.Q...i.e..,...ACCORDING TO QUESTION,

$\sf\large\therefore perimeter\:of\:rectangle= 2 \times (L+B)$

$\sf{\implies 128 = 2 \times (5x +3x) }$

$\sf{\implies 128 = 2 \times (8x) }$

$\sf{\implies 128 = 16x }$

$\sf{\implies 16x=128 }$

$\sf{\implies x= \dfrac{128}{16} }$

$\sf{\implies x= \cancel \dfrac{128}{16} }$

$\sf\large { x=8 }$

$\sf{\boxed{\sf{x=8}}}$

$\sf\therefore substituting\:value\:of\:x\:in\:eq^1\:and\:eq^2$

$\Large\underline\bold{we\:get,}$

$\sf\therefore LENGTH = 5x = 5 \times (8) = 40 m$

$\sf\therefore BREADTH = 3x = 3 \times (8) = 24m$

NOW FINDING THE AREA OF RECTANGLE,

now,

$\sf\large\therefore area\:of\:rectangle= Length \times Breadth$

$\rm{\implies 40 \times 24 }$

$\sf{\boxed{\sf{area = 960 m^2}}}$

$\Large\underline\bold{\therefore area\:of\:park\:is\:960m^2}$

!!___________________!!

ADDITIONAL INFORMATION,

basic info,

• rectangle is a quadrilateral
• whose opposite sides are parllel
• the opposite sides are equal to each other
• to find diagonal of the rectangl,

the formula used is,

$\sf{\boxed{\sf{\therefore diagonal= \sqrt{a^2+b^2}}}}$

$\Large\underline\bold{DIAGRAM,}$

Rectangle

$\setlength{\unitlength}{1.6mm}\begin{picture}(5,6)\put(0,25){\line(1,0){35}}\put(0,0){\line(1,0){35}}\put(0,0){\line(0,1){25}}\put(35,0){\line(0,1){25}}\put(17,-2){breadth}\put(18,-2){}\put(35,15){length}\put(18,0){ }\end{picture}$