Length of a diagonal of a rectangle is10 cm . I ts length is 4/3 times its breadth. Find the area of the square whose perimeter is equal to this rectangle
Answers
Answer:
hope it is helpfull to you
Step-by-step explanation:
Length = (Diagonal) 2 −(Breadth)
2= (10) 2 −(6) 2
= 100−36
= 64
=8cm
Given data :
- Length of a diagonal of a rectangle is 10 cm.
- Its length is 4/3 times its breadth.
- Perimeter of square is equal to perimeter of rectangle.
To find : The area of the square ?
Solution : Let, diagonal of rectangle be D and length of rectangle be L and breadth of rectangle be B.
⟹ D = 10 cm ......( 1 )
⟹ L = 4/3 * B .......( 2 )
Property of rectangle : Each vertex of the rectangle has an angles equal to 90°.
Let,
- 1st side = length ( L )
- 2cd side = breadth ( B )
- Hypotenuse = diagonal
Now, by pythagorus theorem,
⟹ (Hypotenuse)² = (1st side)² + (2cd side)²
⟹ D² = L² + B²
{from eq. ( 1 ) and eq. ( 2 )}
⟹ 10² = ( 4/3 * B )² + B²
⟹ 100 = 16/9 * B² + B²
⟹ 100 = (1 + 16/9) * B²
⟹ 100 = ({9 + 16}/9) * B²
⟹ 100 = 25/9 * B² i.e.
⟹ B² = 100 * 9/25
⟹ B² = 4 * 9
⟹ B² = 36
⟹ B = √36
⟹ B = 6 cm
Now put value of B (breadth) in eq. ( 2 )
⟹ L = 4/3 * B
⟹ L = 4/3 * 6
⟹ L = 24/3
⟹ L = 8 cm
Hence, length and breadth of rectangle is 8 cm and 6 cm respectively.
Now, according to given, we know that, perimeter of square is equal to perimeter of rectangle, so by formula of perimeter of square and perimeter of rectangle.
⟹ 4 * side = 2 ( L + B )
⟹ 4 * side = 2 ( 8 + 6 )
⟹ 4 * side = 2 * 14
⟹ 4 * side = 28
⟹ side = 28/4
⟹ side = 7 cm
Now, by formula of area of square,
⟹ Area of square = ( side )²
⟹ Area of square = ( 7 )²
⟹ Area of square = 49 cm²
Answer : Hence, area of square is 49 cm².
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