the length of a rectangle exceeds its breadth by 9 CM if the length and breadth are increased by 3 cm the area of new rectangle will be 84 CM² more than that of the given rectangle find the length and breadth of the given rectangle check your solution.
Answers
Answer:
Length = 17 cm and breadth = 8 cm
explanation:
Solution -
Let the breadth of the given rectangle = x cm
Then, its length = ( x + 9 )
rectangle}area of the given rectangle
= length × breadth
((x + 9)
((x+9)×x)cm
2
New breadth = ( x + 3 ) cm
New length = [( x + 9 ) + 3 ] cm
=> ( x + 12 ) cm
area of new rectangle
= length × breadth
((x + 12)(x + 3))
according to question
(area of the new rectangle) - ( area of given rectangle ) = 84 sq. cm
} = > (x + 12)(x - 3) - x(x + 9) = 84 \\ = > 6x + 36 = 84 \\ = > 6x = 48
=>(x+12)(x−3)−x(x+9)=84
=>(x
2
+15x+36)−(x
2
+9x)=84
=>6x+36=84
=>6x=48
=>x=
6
48
=>x=8
Thus, the breadth = 8 cm
And, length = ( 8 + 9 ) cm = 17 cm.
In the given rectangle, we have
length = 17 cm , breadth = 8 cm.
Area of given rectangle = ( 17 × 8) sq.cm
136 {cm}^{2}136cm
2
The new length = ( 17 + 3 ) cm = 20 cm,
new breadth = (8 + 3 ) cm = 11 cm.
The area of new rectangle = ( 20 × 11 ) sq.cm
= > 220 {cm}^{2}=>220cm
2
Now,
(area of the new rectangle) - ( area of given rectangle ) 84 sq.cm
= > (220 - 136) = > 84 {cm}^{2} = 84
=>(220−136)cm
=84cm
LHS = RHS
So, Length = 17 cm and breadth = 8 cm
Answer:
let the breath of the given rectangle=x cm
Then its length =(x+ 9) cm
Area of the given rectangle=[x(x+9) ]cm²
New breadth =(x+3)cm
New length =[(x+9) +3] CM =(x+12) cm
So, area of new rectangle =
length × breadth =[(x+12)(x+3)]cm²
(area of new rectangle) -( area of given rectangle)
(x+12) (x+3) -x(x+9) =84
(x²+15x+36) -(x²+9x) =84
6x+36=84
6x=48
Thus,
Breath=8cm
Length=(8+9) cm=17cm
Check:
in the given rectangle, we have
L=17cm
B=8cm
Area of given rectangle=(17×8) =136cm²
the new length =(17+3) =20cm
new breath=8+3=11cm
The area of the new rectangle=(20×11) =220cm²
Now,
(220-136) cm²
=84cm²
Which is the same as given