Question

Rizwan gave his younger sister a rectangular sheet of paper. He halved it by folding it at the mid-point
of its longer side. The piece of paper again became a rectangle whose longer and shorter sides were
in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of
the original rectangle was 4 cm, find the diagonal of the smaller rectangle​

Answer 1

Answer:

2√6 cm

Step-by-step explanation:

Concept: Geometry

Given: Measurements of the Rectangular sheet.

To find: The diagonal of the smaller rectangle created by folding the sheet.

Explanation:

Rizwan gave his younger sister a rectangular sheet of paper. He halved it by folding it at the mid-point of its longer side. The piece of paper again became a rectangle whose longer and shorter sides were in the same proportion as the longer and shorter sides of the original rectangle and the shorter side of the original rectangle was 4 cm. We have to find the diagonal of the smaller rectangle.

Let the length of the bigger(initial) rectangle be = a

Let the breadth of the bigger(initial) rectangle be = b

Therefore by folding the rectangle the length will be halved but the breadth will remain the same.

Length of the smaller rectangle = a/2

Breadth of the smaller rectangle= b

Now it is given that the longer and shorter sides of the smaller rectangle is proportionate to the longer and shorter sides of the larger rectangle.

⇒ a/b = b/(a/2)

⇒a²/2 = b²

Now it is given that b=4cm. Putting the values we get:-

⇒a² = 2×4²

⇒a² = 32

⇒a = √32

⇒a = 4√2

Now the formula of the diagonal of a rectangle is :-

√(length)²+(breadth)²

length of smaller rectangle=2√2

breadth of smaller rectangle=4

Diagonal= √(2√2)²+(4)²

              ⇒√8+16

             ⇒√24

             ⇒2√6 cm (answer)

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