If diagonal of a rectangle is √153 cm and it is given that length of rectangle is four times its breadth and find area of the rectangle
pls give the answer in step by step explanation
Answers
Given :-
• The diagonal of a rectangle is √153 cm
• The length of the rectangle is 4 times its breadth .
To find :-
• The area of the rectangle.
Solution :-
Let the breadth of the rectangle be X cm
Length of the rectangle
= 4 times its breadth
= 4X cm
We know that
The diagonal of a rectangle is
d = √(l²+b²) units
Given that
The diagonal of the rectangle = √153 cm
Therefore, √(l²+b²) = √153
=> √[(4X)²+(X)²] = √153
On squaring both sides then
=> [√{(4X)²+(X)²}]² = (√153)²
=> (4X)²+X² = 153
=> 16X²+X² = 153
=> 17X² = 153
=> X² = 153/17
=> X² = 9
=> X = ±√9
=> X = ±3
Since, X can't be negative.
Therefore, X = 3 cm
Breadth of the rectangle = 3 cm
If X = 3 cm then Length = 4X
= 4(3)
= 12 cm
We know that
Area of a rectangle = length×breadth sq.units
Area of the given rectangle
= 12×3
= 36 cm²
Answer :-
Area of the given rectangle is 36 cm²
Check :-
We have,
Length = 12 cm
Breadth = 3 cm
Length = 4×3 = 4 times the breadth
Diagonal = √(l²+b²) units
=> d = √(12²+3²) cm
=> d = √(144+9) cm
=> d = √153 cm
Verified the given relations in the given problem.
Used formulae:-
• The diagonal of a rectangle is d = √(l²+b²) units
• Area of a rectangle = length×breadth sq.units
Step-by-step explanation:
Given :-
• The diagonal of a rectangle is √153 cm
• The length of the rectangle is 4 times its breadth .
To find :-
• The area of the rectangle.
Solution :-
Let the breadth of the rectangle be X cm
Length of the rectangle
= 4 times its breadth
= 4X cm
We know that
The diagonal of a rectangle is
d = √(l²+b²) units
Given that
The diagonal of the rectangle = √153 cm
Therefore, √(l²+b²) = √153
=> √[(4X)²+(X)²] = √153
On squaring both sides then
=> [√{(4X)²+(X)²}]² = (√153)²
=> (4X)²+X² = 153
=> 16X²+X² = 153
=> 17X² = 153
=> X² = 153/17
=> X² = 9
=> X = ±√9
=> X = ±3
Since, X can't be negative.
Therefore, X = 3 cm
Breadth of the rectangle = 3 cm
If X = 3 cm then Length = 4X
= 4(3)
= 12 cm
We know that
Area of a rectangle = length×breadth sq.units
Area of the given rectangle
= 12×3
= 36 cm²
Answer :-
Area of the given rectangle is 36 cm²
Check :-
We have,
Length = 12 cm
Breadth = 3 cm
Length = 4×3 = 4 times the breadth
Diagonal = √(l²+b²) units
=> d = √(12²+3²) cm
=> d = √(144+9) cm
=> d = √153 cm