1). 5 times a number is equal to 3 times 8 more than the
number. Find the number.
________________________________________________
2). Length of rectangle is 3cm longer than breadth when
length is increased by 5 cm and breadth is doubled
it becomes a square. Find the length and breadth of
rectangle.
_________________________________________________
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Answers
Step-by-step explanation:
Solutions:-
1)
Let the number be X
5 times the number = 5×X = 5X
3 times the number = 3×X = 3X
According to the given problem
5 times the number = 3 times the number +8
=> 5X = 3X+8
=> 5X-3X = 8
=> 2X = 8
=> X = 8/2
=> X = 4
Therefore, X = 4
Answer:-
The required number is 4
Check:-
5 times the number
= 5×4
= 20
3 times the number + 8
= 3×4+8
= 12+8
= 20
Both are equal.
Verified the given relations in the given problem.
2)
Let the breadth of a rectangle be X cm
Then , the Length of the rectangle
= breadth+3 cm
Therefore, Length = (X+3) cm
If the length is increased by 5 cm then the length becomes (X+3+5) cm
= (X+8) cm
If the breadth is doubled then the breadth becomes 2X cm
Given that
If the length is increased by 5 cm and breadth is doubled then it becomes a square.
We know that
All sides are equal in a square
=> length = breadth
=> 2X = X+8
=> 2X-X = 8
=> X = 8 cm
Now,
If X = 8 cm then X+3 = 8+3 = 11 cm
Therefore, length = 11 cm and breadth
= 8 cm
Answer :-
Length of the rectangle = 11 cm
Breadth of the rectangle = 8 cm
Check:-
Length = 11 cm
Breadth = 8 cm
Length = 11 = 8+3 cm
Length = breadth + 3 cm
According to the given problem
If the length is increased by 5 cm then it becomes 11+5 = 16 cm
and If the breadth is doubled then it becomes 2×8 = 16 cm
We have
Length = breadth
So given rectangle becomes a square.
Verified the given relations in the given problem.
Answer:
Heyy Sree Nanda!! How r u??
Borahae❤ (why doesn't purple heart come here?!)
1)
Let the number be x
ATQ
5 × x = 3 (8+x)
3 (8 + x) = 5x
24 + 3x = 5x
24 = 5x - 3x
2x = 24 (i just exchanged their places)
x = 24/2
x = 12
Hence the number is 12.
Hope this is correct!
2)
Let the breadth of rectangle be x cm
Then, Length = (x + 3) cm
Area of rectangle = l × b
= x(x + 3) cm² ... eq1
Also given that length is increased by 9 cm
= (x + 3) + 9 = x + 12 cm
Also given that breadth is reduced by 5 cm
= (x - 5) cm
Area of rectangle = l×b
= (x + 12) (x + 5) ... eq2
From eq1 and eq2 we get:
x(x + 3) = (x + 12) (x - 5)
x² + 3x = x² + 7x - 60
4x = 60
x = 60/4
x = 15
Hence the value of breadth = 15cm
Length = (x + 3) = 15 + 3 = 18cm
Hope that's correct too
Thank you
Saranghaeyo!