Question

3.For a rectangle , the length and breadth are increased by 10% and 20% respectively the percentage increase in area is :

Answer 1

Question:

For a rectangle , the length and the breadth are increased by 10% and 20% respectively , then find the percentage increase in area .

Answer:

The area of the rectangle will be increased by 32% .

Note:

• A rectangle is a parallelogram whose opposite sides are equal.

• Both the diagonals of a rectangle are equal and bisect each other.

• The area of a rectangle of length "L" and breadth "B" is given by;

A = length•breadth = LB.

• The percentage increase is given by; (Final - Initial)•(100/Initial) %

Solution:

Let the initial length of the rectangle be L and the initial breadth of the rectangle be B.

Thus;

The initial area of the rectangle will be;

A = LB

Now,

Let the final length of the rectangle be L' and the final breadth of the rectangle be B'.

Also,

It is said that, the length and the breadth are increased by 10% and 20% respectively.

Thus;

The final length of the rectangle will be;

=> L' = L + 10% of L

=> L' = L + (10/100)L

=> L' = L + (1/10)L

=> L' = L + L/10

=> L' = (10L + L)10

=> L' = 11L/10

Also,

The final breadth of the rectangle will be;

=> B' = B + 20% of B

=> B' = B + (20/100)B

=> B' = B + (1/5)B

=> B' = B + B/5

=> B' = (5B + B)/5

=> B' = 6B/5

Hence,

The final area of the rectangle will be;

=> A' = L'B'

=> A' = (11L/10)(6B/5)

=> A' = 66LB/50

=> A' = 66A/50 { A = LB }

Now,

The percentage increase in the the area of the rectangle will be given by ;

=> (A' - A)(100/A) %

=> (66A/50 - A)(100/A) %

=> { (66A - 50A)/50 }(100/A) %

=> (16A/50)(100/A) %

=> (16/50)•100 %

=> 16•2 %

=> 32 %

Hence,

The area of the rectangle will be increased by 32% .

Answer 2

AnswEr :

• Change in Length = 10%
• Change in Breadth = 20%
• %Increase in Area = ?

$\longrightarrow \mathsf{Change\% = (L + B) + \dfrac{(L \times B)}{100} }$

$\longrightarrow \mathsf{Change\% = (10 + 20) + \dfrac{(1 \cancel0 \times 2 \cancel0)}{ \cancel{100}} }$

$\longrightarrow \mathsf{Change\% = (10 + 20) + 2}$

$\longrightarrow \mathsf{Change\% = 30 + 2}$

$\longrightarrow \mathsf{Change\% = 32\%}$

⠀

$\therefore$ Change in Percentage of New Area of Rectangle is 32%.

⠀

$\large\underline{\mathfrak{Some\: Information\: about\: Rectangle}}$

⋆ Opposite sides are equal and parallel.

⋆ All angles are equal to 90 degrees.

⋆ The diagonals are equal and bisect each other.

⋆ The intersection of the diagonals is the circumcentre. That is you can draw a circle with that as centre to pass through the four corners.

⋆ Any two adjacent angles add up to 180 degrees.

⋆ Lines joining the mid points of the sides of a rectangle in an order form a rhombus of half the area of the rectangle.

⋆ The sum of the four exterior angles is 4 right angles.

⋆ Area of Rectangle = Length * Breadth

⋆ Perimeter of Rectangle = 2*(Length + Breadth)