Question

13. Find the areas of all possible rectangles whose
sides are only positive integer values, given that the
perimeter of each of the rectangles is 18 cm.
14. If the area of a rectangle is 24 sq. cm, find all the
possible dimensions for a rectangle such that the
lengths of the sides are only positive integral values
and also find their perimeters.​

Answer 1

$\bold\pink{\fbox{\sf{Solutions}}}$

13) Actually there can be infinite number of rectangles. Lemme explain,

perimeter = 2(L +B) = 18

⇒L +B = 9

now, we can take any positive number, can be fraction also.

It should be noted that L or B cannot be Zero, because if it is zero, then rectangle could not be formed.

If it is asked, the length and breadth can only be a natural number, then possible dimensions are (length,breadth) as (8,1), (7,2),(6,3),(5,4)

then only 4 rectangles are possible

Otherwise, infinite number of rectangles are possible.

14) With a 24 cm string you need to have 2 lengths and 2 widths covered.

2(l+w)=24.

So l+w=12.

The set of length and widths that satisfy this are (11,1),(10,2),(9,3),(8,4),(7,5),(6,6).

The last one will turn out to be a square a specific case of rectangle.

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