Question

Find the area of rectangle whose perimeter is 100 cm and length and breadth are in the ratio 3 : 2.​

Answer 1

Answer:

let the length be 3x and breadth be 2x

perimeter = 100cm

3x +3x +2x +2x = 100cm

10x = 100cm

x = 10cm

Lenght= 30cm, breadth= 20cm

area= 30× 20cm = 600cm²

Answer 2

GIVEN :-

• Perimeter of rectangle = 100 cm
• Ratio of length and breadth = 3 : 2

TO FIND :-

• The Area of the rectangle

SOLUTION :-

Let the ratio constant be x. Then Length becomes " 3x " and breadth becomes " 2x "

The Perimeter of a rectangle is given by ,

$\\ \star \: \boxed{\purple{\sf{Perimeter = 2 ( Length + Breadth)}}}$

Substituting the values we have ,

$\\ :\implies \sf \: 100 = 2(3x + 2x)$

$\\ : \implies \sf \: 100 = 2(5x)$

$\\ : \implies \sf \:100 = 10x$

$\\ : \implies \boxed{\pink{\sf{x = 10}}}$

Then the values of Length and breadth are ,

$\\ \longmapsto \sf \: length = 3x = 3(10) = 30 \: cm$

$\\ \longmapsto \sf \: breadth = 2x = 2(10) = 20 \: cm$

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Now , Area of rectangle is given by ;

$\\ \star \: \boxed{\purple{\sf{Area = Length \times Breadth}}}$

$\\ : \implies \sf \: Area = 30 \: cm \times 20 \: cm$

$\\ : \implies \sf \: Area = (30 \times 20) \: {cm}^{2}$

$\\ : \implies \boxed{\pink{\sf {\: Area = 600 \: cm {}^{2} }}} \: \bigstar$

$\\ \underline{\sf{Hence\: , The\: Area\:of\:the\:rectangle\:is\: \bold{600\:cm^2}}}$