Question

the area of rectangle is 3000sq.m its sides are in the ratio 6:5,then its perimeter is​

Answer 1

Step-by-step explanation:

GIVEN:-

THE AREA OF RECTANGLE = 3000sq.m

ITS SIDES ARE IN RATIO = 6:5

FORMULAS USED:-

PERIMETER OF RECTANGLE = 2( L+ B)

STEPS TO PROCEED:-

AREA OF RECTANGULAR COURTYARD

= LENGTH X BREADTH

STEPS:-

L : B = 6:5

$l = \frac{6}{5} b$

$3000 = \frac{6}{5} bxb$

$\frac{15000}{6} = b ^{2}$

$b ^{2} = 2500 \\ b = 50 \\ l = \frac{6}{5} b = \frac{6}{5} x50$

L = 60

PERIMETER OF RECTANGULAR COURTYARD

= 2(l+b)

= 2(60+50)

220m

Answer 2

${\large{\underbrace{\underline{\bf{Required~Answer:-}}}}}$

$\underline{\underline{\frak{\red\dag\;Given :}}}$

• Area of rectangle = 3000 m²
• Length:Breadth = 6:5

$\underline{\underline{\frak{\red\dag\;Solution:}}}$

• In this question, we would first find the value of the length and breadth by using the given ratio of sides and the area.

• After finding the sides, we would use the formula of perimeter so as to find the final answer.

» Finding the sides :

We know,

• Length : Breadth = 6 : 5

Let the ratios be 6x & 5x so,

• Length = 6x
• Breadth = 5x

And,

• Area = 3000 m²

Using the formula for finding the Area of rectangle.

$\dashrightarrow \boxed{ \sf \: area _{ \: rectangle} = length \times breadth }$

Put the values..

$\colon \rarr \: \sf \cancel{3000 }\: {m}^{2} = \cancel 6x \times 5x \\ \\ \colon \rarr \sf \: \cancel{500} \: {m}^{2} = \cancel5 {x}^{2} \\ \\ \colon \rarr \: \sf {x}^{2} = 100 \: {m}^{2} \\ \\ \colon \rarr \sf \: x = \sqrt{100 \: {m}^{2} } \\ \\ \colon \rarr \bf\: \pink{x = 10 \: m}$

So,

$\mapsto \sf \: length = 6x = 6 \times 10 \: m \\ \\ \leadsto \boxed{ \tt{ \purple{\: length} = \bf{60 \: m \: }}}$

And,

$\mapsto \sf \: breadth = 5x = 5 \times 10 \: m\\ \\ \leadsto \boxed{ \tt{ \blue{breadth} = \bf50 \: m}}$

» Finding the perimeter :

We know

• Length = 60 m
• Breadth = 50 m

Using the formula for finding the perimeter..

$\dashrightarrow \boxed{ \sf \: perimeter _{rectangle} = 2 \times (length + breadth)}$

Put the values..

$\colon \implies \sf \: perimeter _{ \: rectangle} = 2 \big(60 + 50 \big) \: m \\ \\ \colon \sf \implies \: perimeter _{ \: rectangle} = 2 \times 110 \: m \\ \\ \colon \implies \boxed{ \tt{ \red {perimeter _{ \: rectangle} = \bf{ \pink{220}\: m}}}}$

So,

★ The Perimeter of the rectangle would be 220 m.

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