# Definition Rectangle

Definition of Rectangle:

Rectangle is a quadrilateral which has equal opposite sides and all angles are right angles, not all sides are equal only the pair of opposite sides are equal.

Rectangles are a parallelogram in which adjacent sides are perpendicular to each other i.e every angle is equal to 900.

A square is a special case of rectangles which has all four sides are equal to each other.

Properties of rectangles:-

• Rectangles are cyclic.
• Rectangles are equiangular.
• Rectangles are vertex transitive.
• The diagonals are bisecting each other.
• The diagonals are equal to each other.

## Formulas Related to Rectangle:-

Area of Rectangle = Length(l) * Breadth(w)

Length of diagonals = √ (l2 + w2)

A rectangle has circum-circle with circum-radius R = ½√ (l2 + w2)

Example:

Question: Find the area and perimeter of a rectangle that’s side measures as 5cm and 8cm.

Solution:

Area of Rectangle = Length * Breadth

= 5*8

= 40 cm2

= 2(5+8)

= 26 cm

## Problems on Rectangles:-

Questions1: Find the area and perimeter of a rectangle that’s side measures as 6cm and 8cm. and also find the length of diagonal.

Solution:

Area of Rectangle = Length * Breadth

= 6*8

= 48 cm2

= 2(6+8)

= 28 cm

Length of diagonals = √ (l2 + w2)

= √(36+64)

= 10 cm

Questions2:Find the measure of length and breadth of a rectangle that’s area is 84 cm2 and Perimeter is given as 38 cm.

Solution:

Area of Rectangle = Length * Breadth

84 = l*b    ------- (i)

38 = 2(l+b)

19 = l+b

19-b = l

from (i)

84 = b*(19-b)

84 = 19b-b2

b2 -19b+84  = 0

So, b = 7cm and l = 12 cm.

Questions3: Find the circumradius of a rectangle which has cicumcircle with sides 6 cm and 8 cm.

Solution:

R = ½√ (l2 +w2)

=½√(36+64)

=5 cm

Questions 4: find the circumradius of a rectangle, the sum of square of sides is given as 36 cm.

Solution:

R = ½√ (a2 + b2)

Here (a2 + b2) = 36

R = ½√36

R = 3 cm