if the perimeter of a rectangle, obtained by increasing one side of a square by 2cm and decreasing another side by 2 cm is 64 cm,then find the side of the original square.
Answers
Given data :-
- Increasing one side of a square by 2cm.
- Decreasing another side of square by 2 cm.
- Perimeter of rectangle is 64 cm.
Solution :-
To find the original side of square.
Let, side of square be x and we kniw that all sides of square are equal in length.
Now, accirding to given
→ Length of rectangle, L = { x + 2 } cm
→ Breadth of rectangle, B = { x - 2 } cm
Now, we use formula of perimeter of rectangle
→ Perimeter of rectangle = 2 [ L + B ]
→ 64 = 2 [ x + 2 + x - 2 ]
→ 64 = 2 [ 2x ]
→ 64 = 4x i.e.
→ x = 64/4
→ x = 16 cm
Hence, the original side of square is 16 cm.
More info :
Propeties of rectangle
→ It has four sides and four vertices.
→ Each vertex has angle equal to 90 degrees.
→ The opposite sides are equal and parallel.
→ Diagonal bisect each other.
→ Perimeter is equal to twice of sum of its length and breadth.
→ Area is equal to product of its length and breadth.
→ It’s a parallelogram with four right angles.
→ Sum of all interior angles equal to 360 degrees .
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Answer:
16cm
Step-by-step explanation:
Let the side of the original square be x.
One side is increased by 2cm i.e. x+2
Another side is decreased by 2cm i.e. x-2
Now the rectangle formed thus has length (x+2) and breadth (x-2).
So using simple formula of perimeter of rectangle
Perimeter=2(length + breadth)
=2[(x+2) + (x-2)]
=2(x+2+x-2)
=2(2x)
=4x.
Now given perimeter is 64cm.
So
4x=64
x=64/4
x=16..
Hope this helps !! Thanks!