Question

A rectangle is 14cm long and 10cm wide. If the length is reduced by x cms and its width is increased also by x cms so as to make it a square. Find the change in the area (rounded to first decimal place).

Answer 1

Answer:

Change in area is 4.0 cm^2.

Step-by-step explanation:

Lengths of rectangle = 14 cm

Breadth of rectangle = 10 cm

Thus,

Area of rectangle ( Using area of rectangle = length x breadth ) = 14 cm x 10 cm = 140 cm^2

If length of reduced by x cm and its width is increased also by x cm so as to make it a square, then, now, length of rectangle is 14 cm - x cm & breadth of rectangle is 10 cm + x cm.

Since new sides form a square, their lengths must be equal = > 10 cm + x cm = 14 cm - x cm

= > Length of side of square

= > 10 cm + x cm = 14 cm - x cm

= > 2x cm = 4 cm

= > x cm = 2 cm

Length of side of square = 14 cm - 2 cm = 12 cm.

So,

Area of square = ( 12 cm )^2 = 144 cm { Area of square is square of its side }

= > Change in area = 144 cm^2 - 140 cm^2 = 4.0 cm^2

Hence, change in area is 4.0 cm^2.

Answer 2

AnswEr :

• R E C T A N G L E :

• Length of Rectangle = 14 cm
• Breadth of Rectangle = 10 cm

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\large{A}}\put(7.3,2){\mathsf{\large{10 cm}}}\put(7.7,1){\large{B}}\put(9.2,0.7){\matsf{\large{14 cm}}}\put(11.1,1){\large{C}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\put(11.1,3){\large{D}}\end{picture}$

↠ Area of Rectangle = Length × Breadth

↠ Area of Rectangle = 14 cm × 10 cm

↠ Area of Rectangle = 140 cm²

$\rule{300}{1}$

According to the Question, If we Reduce x cms from the length or, we Increase x cms in width, that will be Side of the Square.

↦ Side of Square

↦ Length – x = Breadth + x

↦ 14cm – x = 10cm + x

↦ 14cm – 10cm = x + x

↦ 4cm = 2x

• Dividing both term by 2

↦ x = 2cm

◗ Side of Square = 14 - x = 14 - 2 = 12 cm

◗ Side of Square = 10 + x = 10 + 2 = 12 cm

$\rule{300}{1}$

• S Q U A R E :

• Side of Square = 12 cm

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\large{A}}\put(7.3,2){\mathsf{\large{12 cm}}}\put(7.7,1){\large{B}}\put(9,0.7){\matsf{\large{12 cm}}}\put(10.6,1){\large{C}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){2}}\put(10.5,1){\line(0,3){2}}\put(8,3){\line(3,0){2.5}}\put(10.6,3){\large{D}}\end{picture}$

↠ Area of Square = ( Side )²

↠ Area of Square = ( 12 cm )²

↠ Area of Square = ( 12 cm × 12 cm )

↠ Area of Square = 144 cm²

$\rule{300}{2}$

• PERCENTAGE CHANGE IN AREA :

$\longrightarrow \tt Change\% = \dfrac{Change}{Old \:Area} \times 100 \\ \\\longrightarrow \tt Change\% = \dfrac{(New \:Area - Old \:Area)}{Old \:Area} \times 100 \\ \\\longrightarrow \tt Change\% = \dfrac{(144 - 140)}{140} \times 100 \\ \\\longrightarrow \tt Change\% = \dfrac{4}{140} \times 100 \\ \\\longrightarrow \tt Change\% = \dfrac{400}{140} \\ \\\longrightarrow \large\boxed{ \red{\tt Change\% =2.85\%}}$

⠀

∴ There will be Change of 2.85% in Area.

#answerwithquality #BAL