Practice Math With Us

Find Dimensions of Rectangle

Introduction to rectangle

Arectangle is a four-sided figure with opposite sides parallel and equaland all angles equal. It can also be defined as a parallelogram with alangles equal.

 Arectangle has a unique length and breadth and all angles are equal to 90 degrees. If the length and breadth of the rectangle becomes equal, the rectangle will become a square

 Dimensionsofrectangle


Please express your views of this topic Rectangle Definition  by commenting on blog. 


How to find dimensions of a rectangle ?


Before we learn how to find the dimensions of a rectangle let us look at the properties of a rectangle in detail. 

  1. A rectangle has opposites equal
  2. A rectangle has every angle equal to 900
  3. A rectangle is completely defined with the length and breadth.

Let us look at how to calculate the area and perimeter of a rectangle

Perimeter:The perimeter of a rectangle is the sum of the length of all four sidesof the rectangle. If the length of the rectangle is l and breadth of the rectangle is b, the the perimeter can be calculated as

Perimeter = Sum of the length of the four sides = length + breadth + Length + breadth.

Opposite sides of a rectangle are equal

So perimeter = 2 Length + 2 breadth = 2 (length + breadth) = 2(l+b)

Perimeter has the same units as that of length like millimeter (mm), centimeter (cm) or meter (m)

Area: Area is the measure of the space enclosed by the rectangle. Area of a rectangle is calculated by the formula

Area = length x breadth

A = l x b

The area of the rectangle has the units of square of distance like millimeter squared (mm2) or centimeter squared (cm2) or meter squared (m2)

Giventhe area and perimeter of a rectangle, we can find the dimensions of a rectangle. By dimensions we mean th length and the breadth. Let us solvesome examples on this

Ex 1: Find the dimensions of a rectangle  if  the perimeter of a rectangle is 14 cm and the area of the rectangle is 10 cm2..

Sol: Let the length of the rectangle = l

And let the breadth of the rectangle = b

Step 1: Perimeter = 2(l+b) = 14

Step 2: Area = l x b = 10

Step 3: l+b = 14/2 = 7

Step 4: lb =10

Step 5: Find two numbers whose sum is 7 or product is 10

 By trial and error we get numbers as 5 and 2

Length = 5cm  and Breadth = 2cm

Dimensions of the rectangle is 5 cm x 2 cm

Note: To solve the set of equation

Step 6: I+b = 7 and lb = 10 mathematically, we can use the identity

Step 7: (l-b)2 = (l+b)2 – 4lb

Step 8: (l-b)2 = 72 – 4 x 10 = 49-40 =9

Step 9: l-b = `sqrt(9)`  =  3 or –3

If l-b = 3 and l+b = 7 then l = 5 and b="2

If l-b = -3 and l+b = 7 then l = 2 and b="5

Weget the same set of values. By convention length is assumed to be greater than the breadth hence we choose length to be 5 cm and breadth to be 2 cm

Ex 2: Find the dimensions of a rectangle whose length is 3cm more than the breadth and the perimeter is 34 cms.

Sol: Let the length of the rectangle = l

And let the breadth of the rectangle = b

Step 1: Perimeter = 2(l+b) = 34

Step 2: l+b = 17

Step 3: Given, Length = breadth + 3 or l="b+3

 b+3+b = 17

Step 4: 2b+3=17

Step 5: 2b="17-3" = 10

Step 6: b="10/2" = 5

Step 7: l="b+3" = 7+3= 10

Length of the rectangle = 10 cm and breadth of the rectangle = 7 cm

Dimensions of the rectangle is 10 cm x 7 cm

Note : Always mention the units appropriately else the answer is incomplete. 


Between, if you have problem on these topics Translation in Math ,please browse expert math related websites for more help on answer my math questions .


Exercise on finding dimensions of a rectangle


Let us summarize the properties of a rectangle. A rectangle has 

  • Opposite sides parallel and equal
  • All angles equal and each angle is equal to 900
  • Length and breadth as its dimensions
  • Twice the sum of length and breadth as the perimeter
  • Product of length and breadth as the area

 Let us try some exercises on how to find dimensions of a rectangle

Pro 1: Find the dimensions of a rectangle if the breadth of a rectangle is half that of the length and the area of the rectangle is 50 cm2.

Ans: 10 cm x 5cm 

Pro 2: Find the dimensions of some rectangles with area of 100 cm2. Whichof these will have  the minimum perimeter? (Hint: If the perimeter is minimized for a given are, the rectangle will become a square with equallength and breadth)

Ans: 10 cm x 10 cm  

Pro 3: If the length of rectangle is doubled and the breadth is halved, how will the area and perimeter get affected?

Ans: Area will remain the same , perimeter will increase assuming length is greater than the breadth.