Question

2. Draw a rectangle with an area of 20 sq.cm and perimeter 24 cm.​

Answer 1

answer

We know that perimeter of a rectangle is 2(l + b)

Given, Perimeter = 2(l + b) = 20cm

=> l + b = 20/2

=> l + b = 10cm ...........(i)

We know that area of a rectangle = length × breadth

Given, Area = L × B = 24

=> lb = 24........(ii)

Now,

squaring both sides in (i) equation

(l + b)² = (10)²

=> l² + b² + 2lb = 100

putting value of lb we get

=> l² + b² + 2(24) = 100

=> l² + b² + 48 = 100

=> l² + b² = 100 - 48

=> l² + b² = 52

Now subtracting 2lb from both sides,

l² + b² - 2lb = 52 - 2lb

Putting value of lb in RHS

l² + b² - 2lb = 52 - 2(24)

=> l² + b² - 2lb = 4

We can write,

(l - b)² = (2)²

=> l - b = 2 ........(iii)

Adding (i) and (iii)

l + b + l - b = 10 + 2

=> 2l = 12

=> l = 12/2 = 6

\boxed{Length \:= \:6cm}

Length=6cm

Putting l in (i)

l + b = 10

=> 6 + b = 10

=> b = 10 - 6 = 4cm

\boxed{Breadth\: =\: 4cm}

Breadth=4cm

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Answer 2

Answer:

The perimeter of a rectangle is given by 2(l+b) , where l is length and b is breadth of the given rectangle.

From the given problem statement, we get l+b=12 .

Area of the rectangle is given by lb .

Assuming real numbers for the sides of the rectangle, we get infinite number of values for the area.

For example, let b=0.001 , then l=11.999 . Then the area becomes area=0.011999cm2.