the length of a rectangle is greater than the breadth by 18 cm. if both length and breadth are increased by 6
cm, then area increases by 168 cm square. find the length and breadth of the rectangle
Answers
Answer:
Step-by-step explanation:
Let the breadth of the rectangle be x.
Then the length of the rectangle will be greater than the breadth by 18cm = (x+18) cm.
We know that Area of the rectangle = l * b
= x * (x + 18)
= x^2 + 18x ------------- (1)
Given that breadth of the rectangle is increased by 6cm. = (x+6)cm.
Then the length of the rectangle = (x + 6 + 18)
= (x + 24).
Now the area of the rectangle = (x + 6)(x + 24)
= x^2 + 24x + 6x + 144
= x^2 + 30x + 144 ------------ (2)
On solving (1) and (2) with the increased area by 168cm^2.
x^2 + 18x + 168 = x^2 + 30x + 144
18x + 168 = 30x + 144
12x = 24
x = 2.
If the breadth is 2cm Then the length will be (2 + 18) = 20cm.
Therefore the length = 20cm and the breadth = 2cm.
Hope this helps!
Given:-
breadth:-b
length (l):-b+18
Area:-b×(b+18)
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Find:-
Find the length and breadth of the rectangle
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Solution:-
if both length and breadth increased by 6,new dimension.......
new Breadth:-b+6
new Length:-b+18+6
(New Area=Area+168)
BREADTH:-
=>(b+6)×(b+24)=(b×(b+18))+168
=>b2+24b+6b+144=b2+18b+168
=>30b-18b=168-144
=>12b=24
=>b=2 cm
LENGTH:-
l=b+18
l=2+18
l=20 cm
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Answer:-
Length:-20 cm
Breadth:-2 cm
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Formula used:-
Area=length×breadth