Answer:
Given :
The diagonal of a rectangle is 2 ✓13 cm.
The length and breadth are in the ratio
3:2.
To find :
The Area of the rectangle.
Solution :
Given that
The ratio of the length and breadth of a rectangle = 3:2
Let they be 3X cm and 2X cm
We know that
The diagonal of a rectangle = √(1²+b³)
units
The diagonal of the rectangle
= √[(3X)³+(2X)³] cm
= √(9x³+4x²) cm
=> √(13X²) cm
=> √13 X cm
According to the given problem
The diagonal of the rectangle = 2√13 cm
=> ✓13 X = 2 √13
=> X = 2√13/√13
=> X = 2 cm
If X = 2 cm then 3X=3(2) = 6 cm
If X = 2 cm then 2X = 2(2)=4 cm
Length = 6 cm
Breadth = 4 cm
We know that
Area of a rectangle = length breadth sq.units
Area of the given rectangle = 6 cm x 4 cm
= 24 cm²