The perimeter of a rectangle is 140cm.If the sides are in the ratio 3:4,find the length of the four sides and two diagnals
Answers
Given : -
The perimeter of a rectangle is 140 cm .If the the sides are in the ratio of 3 : 4 .
Required to find : -
- Find the length of four sides and two diagonals ?
Formula used : -
Perimeter of a rectangle = 2 ( length + breadth )
Solution : -
The perimeter of a rectangle is 140 cm .If the the sides are in the ratio of 3 : 4 .
We need to find the length of four sides and two diagonals .
So,
Let's consider the given ratio.
Ratio of the sides = 3 : 4
Let the length be 3x
Breadth be 4x
According to problem ;
Perimeter of the rectangle = 2 ( length + Breadth )
➾ 140 = 2 ( 3x + 4x )
➾ 140/2 = ( 3x + 4x )
➾ 70 = ( 3x + 4x )
➾ 70 = 7x
➾ 7x = 70
➾ x = 70/7
➾ x = 10
Hence,
- value of x = 10
Now,
Let's find the measurement of length & breadth of the rectangle .
This implies ;
Length = 3x = 3(10) = 30 cm
Breadth = 4x = 4(10) = 40 cm
Hence,
- Length of the rectangle = 30 cm
- Breadth of the rectangle = 40 cm
Now,
Let's find out the measurement of the diagonal .
Using Pythagoras theorem ;
( side )² + ( side )² = ( Hypotenuse )²
This can be modified as ;
( length )² + ( breadth )² = ( diagonal )²
By substituting the values we get ;
➾ ( 30 )² + ( 40 )² = ( diagonal )²
➾ 900 + 1600 = ( diagonal )²
➾ 2500 = ( diagonal )²
➾ ( diagonal )² = 2500
➾ diagonal = √2500
➾ diagonal = ±50
➾ diagonal = + 50 or - 50
Since,
Length can't be negative !
Hence,
- Length of the diagonal = 50 cm
Therefore,
The sides of the rectangle are ;
30 , 40 , 30 & 40 cm
The length of diagonals are ;
50 cm & 50 cm
Reasons :
In a rectangle ,
- opposite sides are equal.
- Diagonal bisect each other .
- Diagonals are equal .
Answer:
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