Math, asked by rajanhu621, 6 months ago

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

Answered by anamikavinod27
4

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!

Answered by Vyomsingh
25

Given:-

breadth:-b

length (l):-b+18

Area:-b×(b+18)

_____________________________

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

______________________________

Answer:-

Length:-20 cm

Breadth:-2 cm

______________________________

Formula used:-

Area=length×breadth

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