Question

4. It is printed on a paper that “The length
of a diagonal of a rectangle is 10 cm and its
area is 62.5 sq. cm”. Then which one of the
following statements is true?
(a) The perimeter of the rectangle is
30 cm.
(b) The sum of the length and breadth
is 20 cm.
(c) The difference of the length and
breadth is 5 cm.
(d) No such rectangle can exist.​

Answer 1

Therefore the perimeter of the rectangle is 30 cm. (Option-a )

Given:

The diagonal of the rectangle = d =10 cm

The area of the rectangle = 62.5 cm²

To Find:

Which of the given statements are true?

Solution:

The given question can be solved as shown below.

Let the length of the rectangle = a

Let the breadth of the rectangle = b

Given that,

The diagonal of the rectangle = d =10 cm

The area of the rectangle = ab = 62.5 cm²

In the rectangle, by using Pythagoras theorem,

⇒ d² = a² + b² = 100     (i.)

⇒ ( a + b )² = a² + b² + 2ab

⇒ ( a + b )² = 100 + 2 (62.5)

⇒ ( a + b )² = 100 + 125 = 225

⇒ ( a + b ) = 15

Hence the sum of length an breadth = (a + b) = 15 cm

The perimeter of the rectangle = 2( a + b ) = 2 × 15 = 30 cm

Therefore the perimeter of the rectangle is 30 cm.

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