Question

The Breadth of a rectangle is 4 cm less than its length. If the length is increased by 4 cm and breadth is decreased by 1 cm , the area of the rectangle is increased by 40 cm².Find the length and breadth of the rectangle

Answer 1

Answer:

Length = 20 cm

Breadth = 16 cm

Step-by-step explanation:

Let the length be 'l' cm

Therefore, Breadth will be (l-4) cm

Now, we know that,

Area of rectangle = length × Breadth

=> A = l(l-4)

Now,

According to question,

Length is increased by 4 cm

=> New length, l' = (l+4) cm

Breadth is decreased by 1 cm

=> New breadth = (l-5) cm

Also, Area increased by 40 sq. cm

=> New area = (A+40) sq. cm

=> A' = A + 40

=> (l+4)(l-5) = l(l-4) +40

Therefore, we will get,

$= > {l}^{2} - 5l + 4l - 20 = {l}^{2} - 4l + 40 \\ \\ = > - l - 20 = - 4l + 40 \\ \\ = > 4l - l = 40 + 20 \\ \\ = > 3l = 60 \\ \\ = > l = \frac{60}{3} \\ \\ = > l = 20$

Therefore, length = 20 cm

Thus, Breadth = 20 - 4 = 16 cm

Hence, the required length and breadth are 20 cm and 16 cm respectively.

Answer 2

Answer:

leagth=20cm

breadt=16cm

Step-by-step explanation:

Length = 20 cm

Breadth = 16 cm

Step-by-step explanation:

Let the length be 'l' cm

Therefore, Breadth will be (l-4) cm

Now, we know that,

Area of rectangle = length × Breadth

=> A = l(l-4)

Now,

According to question,

Length is increased by 4 cm

=> New length, l' = (l+4) cm

Breadth is decreased by 1 cm

=> New breadth = (l-5) cm

Also, Area increased by 40 sq. cm

=> New area = (A+40) sq. cm

=> A' = A + 40

=> (l+4)(l-5) = l(l-4) +40

Therefore, we will get,

\begin{gathered}= > {l}^{2} - 5l + 4l - 20 = {l}^{2} - 4l + 40 \\ \\ = > - l - 20 = - 4l + 40 \\ \\ = > 4l - l = 40 + 20 \\ \\ = > 3l = 60 \\ \\ = > l = \frac{60}{3} \\ \\ = > l = 20\end{gathered}

=>l

2

−5l+4l−20=l

2

−4l+40

=>−l−20=−4l+40

=>4l−l=40+20

=>3l=60

=>l=

3

60

=>l=20

Therefore, length = 20 cm

Thus, Breadth = 20 - 4 = 16 cm

Hence, the required length and breadth are 20 cm and 16 cm respectively